PowerShell 5+ cryptographically secure password generator. It's a port of the legacy System.Web.Security.Membership.GeneratePassword(Int32, Int32) function

New-Password.ps1

function New-Password
{
    [CmdletBinding()]
    param
    (
        [Parameter(Mandatory=$true)]
        [ValidateRange(2,128)]
        [int]
        $Length,

        [Parameter(Mandatory=$true)]
        [ValidateRange(0,128)]
        [int]
        $NumberOfNonAlphanumericCharacters
    )
    begin
    {
        # https://referencesource.microsoft.com/#System.Web/Security/Membership.cs,302

        $punctuations = "!@#$%^&*()_-+=[{]};:>|./?".ToCharArray()
    
        $buf   = [byte[]]::new( $Length )
        $cBuf  = [char[]]::new( $Length )
        $count = 0
    }
    process
    {
        if( $NumberOfNonAlphanumericCharacters -gt $Length )
        {
            throw "NumberOfNonAlphanumericCharacters cannot be greater than Length"
        }

        try
        {
            $randomNumberGenerator = [System.Security.Cryptography.RandomNumberGenerator]::Create()

            $randomNumberGenerator.GetBytes($buf)
        }
        catch
        {
            Write-Error "Failed to create an instance of System.Security.Cryptography.RandomNumberGenerator"
            return
        }
        finally
        {
            if( $null -ne $randomNumberGenerator )
            {
                $randomNumberGenerator.Dispose()
            }        
        }
        
        for($iter = 0; $iter -lt $Length; $iter++ )
        {
            $i = [int]($buf[$iter] % 87)
            
            if( $i -lt 10 ) # 0-9
            {
                $cBuf[$iter] = [char]([int][char]'0' + $i - 10)
            }
            elseif( $i -lt 36) # A-Z
            {
                $cBuf[$iter] = [char]([int][char]'A' + $i - 10)
            }
            elseif( $i -lt 62) # a-z
            {
                $cBuf[$iter] = [char]([int][char]'a' + $i - 36)
            }
            else # punctuations
            {
                $cBuf[$iter] = $punctuations[$i-62]
                $count++;
            }
        }

        if( $count -lt $numberOfNonAlphanumericCharacters )
        {
            $j = $k = 0

            $rand = New-Object Random
 
            for( $j = 0; $j -lt $numberOfNonAlphanumericCharacters - $count; $j++ )
            {
                do
                {
                    $k = $rand.Next( 0, $length )
                }
                while( -not [Char]::IsLetterOrDigit( $cBuf[$k] ) )
                

                $cBuf[$k] = $punctuations[$rand.Next(0, $punctuations.Length)]
            }
        }

        return [string]::new( $cBuf )
    }
    end
    {
    }
}

New-Password -Length 13 -NumberOfNonAlphanumericCharacters 4