Android Login app, using Self-Signed SSL Certificate. Later on, I'll create a project at GitHub, with the whole App (explanations and details).

activity_1_login_screen.xml

<?xml version="1.0" encoding="utf-8"?>
<layout>

    <data>
        <variable
            name="handler"
            type="com.ivanlmj.myapp.LoginScreen" />
    </data>

    <LinearLayout
        android:orientation="vertical"
        xmlns:android="http://schemas.android.com/apk/res/android"
        xmlns:tools="http://schemas.android.com/tools"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        android:background="#1a75ff"
        tools:context=".LoginScreen">

        <LinearLayout
            android:orientation="vertical"
            android:layout_marginTop="25dp"
            android:layout_width="match_parent"
            android:layout_height="wrap_content">

            <LinearLayout
                android:orientation="horizontal"
                android:layout_width="wrap_content"
                android:layout_height="150dp"
                android:layout_marginStart="0dp"
                android:layout_marginLeft="0dp">

                <ImageView
                    android:layout_width="110dp"
                    android:layout_height="wrap_content"
                    android:layout_marginTop="10dp"
                    android:layout_marginStart="30dp"
                    android:layout_marginLeft="0dp"
                    android:scaleX="0.8"
                    android:scaleY="0.8"
                    android:src="@drawable/an_image" <!-- must store an image inside ot the drawable directory -->
                    tools:ignore="ContentDescription" />

                <TextView
                    android:layout_width="match_parent"
                    android:layout_height="match_parent"
                    android:layout_marginTop="60dp"
                    android:layout_marginStart="10dp"
                    android:layout_marginLeft="0dp"
                    android:text="MyApp"
                    android:textSize="34sp"
                    android:textColor="#ffffff"/>

            </LinearLayout>

            <LinearLayout
                android:layout_width="match_parent"
                android:layout_height="wrap_content"
                android:background="#1a75ff">

                <TextView
                    android:layout_width="match_parent"
                    android:layout_height="50dp"
                    android:layout_marginTop="20dp"
                    android:gravity="center"
                    android:text="WELCOME"
                    android:textColor="#ffffff"
                    android:textSize="25sp"/>
            </LinearLayout>

        </LinearLayout>

        <LinearLayout
            android:orientation="vertical"
            android:layout_width="match_parent"
            android:layout_height="match_parent">

            <EditText
                android:id="@+id/tjs_login_screen_usuario"
                android:layout_marginTop="30dp"
                android:layout_gravity="center"
                android:layout_height="42dp"
                android:layout_width="270dp"
                android:ems="12"
                android:hint="@string/login_text_user"
                android:inputType="text"
                android:textSize="15sp"
                android:textColorHint="#ffffff"/>

            <EditText
                android:id="@+id/tjs_login_screen_contraseña"
                android:layout_marginTop="10dp"
                android:layout_gravity="center"
                android:layout_height="42dp"
                android:layout_width="270dp"
                android:ems="12"
                android:hint="@string/login_text_password"
                android:inputType="textPassword"
                android:textSize="15sp"
                android:textColorHint="#ffffff"/>

            <Button
                android:id="@+id/tjs_login_screen_button"
                android:layout_marginTop="20dp"
                android:layout_marginStart="0dp"
                android:layout_marginLeft="0dp"
                android:layout_gravity="center"
                android:layout_width="270dp"
                android:layout_height="80dp"
                android:textColor="#ffffff"
                android:onClick="login"
                android:text="@string/login_button_name"
                android:textSize="16sp"/>

        </LinearLayout>

    </LinearLayout>

</layout>

Android SSL (Self-signed certificate)

package com.ivanlmj.myapp;


import android.content.Context;

import android.os.Bundle;

import android.support.v7.app.AppCompatActivity;

import android.util.Log;

import android.view.View;

import android.widget.EditText;
import android.widget.Toast;

import com.android.volley.Request;
import com.android.volley.RequestQueue;
import com.android.volley.Response;
import com.android.volley.VolleyError;
import com.android.volley.toolbox.HurlStack;
import com.android.volley.toolbox.StringRequest;
import com.android.volley.toolbox.Volley;

import java.io.InputStream;
import java.security.KeyStore;
import java.security.cert.Certificate;
import java.security.cert.CertificateFactory;
import java.util.HashMap;
import java.util.Map;

import javax.net.ssl.SSLContext;
import javax.net.ssl.SSLSocketFactory;
import javax.net.ssl.TrustManagerFactory;


public class LoginScreenTest extends AppCompatActivity {

    HurlStack hurlStack   = null;
    EditText  username    = null;
    EditText  password    = null;

    @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_1_login_screen);
        username = (EditText) findViewById(R.id.tjs_login_screen_usuario);
        password = (EditText) findViewById(R.id.tjs_login_screen_contraseña);

        try {
          
            /* To understand the concept about Self-Signed Certificates, Custom TrustManagers, etc.                        
            CertificateFactory:  https://docs.oracle.com/javase/7/docs/api/java/security/cert/CertificateFactory.html
            Certificate:         https://docs.oracle.com/javase/7/docs/api/java/security/cert/Certificate.html
            KeyStore:            https://docs.oracle.com/javase/7/docs/api/java/security/KeyStore.html
            KeyManagerFactory:   https://docs.oracle.com/javase/7/docs/api/javax/net/ssl/KeyManagerFactory.html
            TrustManagerFactory: http://docs.oracle.com/javase/7/docs/api/javax/net/ssl/TrustManagerFactory.html
            SSLContext:          https://docs.oracle.com/javase/7/docs/api/javax/net/ssl/SSLContext.html
            SSLSocketFactory:    https://docs.oracle.com/javase/7/docs/api/javax/net/ssl/SSLSocketFactory.html
            */

            Context myContext     = getApplicationContext();
            InputStream inStream  = myContext.getResources().openRawResource(R.raw.tdmssl);
            // Use the .crt file obtained via this script: https://gist.github.com/ivanlmj/a6a93dd142fb623d01262303d5bd8074
            CertificateFactory cf = CertificateFactory.getInstance("X.509");
            Certificate ca        = cf.generateCertificate(inStream);
            inStream.close();

            String keyStoreType = KeyStore.getDefaultType();
            KeyStore ks = KeyStore.getInstance(keyStoreType);
            ks.load(null, null);
            ks.setCertificateEntry("ca", ca);

            TrustManagerFactory tmf = TrustManagerFactory.getInstance("X509");
            tmf.init(ks);

            SSLContext sslContext = SSLContext.getInstance("TLS");
            sslContext.init(null, tmf.getTrustManagers(), null);

            SSLSocketFactory sslSocketFactory = sslContext.getSocketFactory();
            hurlStack = new HurlStack(null, sslSocketFactory);

        } catch (Exception e){
            Log.d("my_app","LoginScreen.java - SSL Exception: " + e.toString());
            e.printStackTrace();
        }

    }

    public void login(View view) {

        setProgressBarIndeterminateVisibility(true);
        RequestQueue queue = Volley.newRequestQueue(this, hurlStack);
        // In this example, I'm uing Python FLASK with MySQL. 
        // Basically, FLASK performs a query, looking for user + pass in a database (table).
        final String url = "https://127.0.0.1:5000/login";

        StringRequest postRequest = new StringRequest(Request.Method.POST, url,
                new Response.Listener<String>()
                {
                    @Override
                    public void onResponse(String response) {
                        Log.d("my_app", "LoginScreen.java - Request status: SUCCESSFUL");
                        Log.d("my_app", "LoginScreen.java - Response content:" + response);
                        if (response.equals("ok")) {
                            Log.d("my_app", "LoginScreen.java - Login status: SUCCESSFUL");
                            Log.d("tjs_app", "LoginScreen.java - Authenticated User: " + username.getText().toString().trim());
                            Toast.makeText(getApplicationContext(), "Login OK!",Toast.LENGTH_SHORT).show();
                        } else {
                            Log.d("my_app", "LoginScreen.java - Login status: FAIL");
                            Log.d("my_app", "LoginScreen.java - Authentication attempt from: " +  username.getText().toString().trim());
                            Toast.makeText(getApplicationContext(), "Check User or Password.",Toast.LENGTH_SHORT).show();
                        }
                    }
                },
                new Response.ErrorListener()
                {
                    @Override
                    public void onErrorResponse(VolleyError error) {
                        Log.d("my_app", "LoginScreen.java - Request status: FAIL");
                        Log.d("my_app", "LoginScreen.java - Response content:" + error);
                        Toast.makeText(getApplicationContext(), "Check your internet connection.",Toast.LENGTH_SHORT).show();
                    }
                }
        ) {
            @Override
            protected Map<String, String> getParams()
            {
                Map<String, String>  params = new HashMap<String, String>();
                params.put("username", username.getText().toString().trim());
                params.put("password", password.getText().toString().trim());
                return params;
            }
        };
        queue.add(postRequest);

    }

}

HI @ivanlmj any update on this?