Select the points belonging to a given checkpoint area. First, I create the tables checkpoint and point. Then, two checkpoints are created, and five points are inserted. Finally, I define the query that fulfill the statement.

gistfile1.sql

CREATE TABLE public.checkpoint (
  id SERIAL PRIMARY KEY,
  geom GEOMETRY(Point, 26910),
  radio int,
  name VARCHAR(128)
);

CREATE INDEX public.checkpoint_geom_index
  ON public.checkpoint
  USING GIST (geom);

INSERT INTO public.checkpoint (geom, radio) VALUES (
  ST_GeomFromText('POINT(0 0)', 26910),
  50
);

INSERT INTO public.checkpoint (geom, radio) VALUES (
  ST_GeomFromText('POINT(100 100)', 26910),
  50
);


CREATE TABLE public.point (
  id SERIAL PRIMARY KEY,
  geom GEOMETRY(Point, 26910)
);

CREATE INDEX public.point_geom_index
  ON public.point
  USING GIST (geom);

INSERT INTO public.point (geom) VALUES (
  ST_GeomFromText('POINT(0 0)', 26910)
);

INSERT INTO public.point (geom) VALUES (
  ST_GeomFromText('POINT(0 25)', 26910)
);

INSERT INTO public.point (geom) VALUES (
  ST_GeomFromText('POINT(0 50)', 26910)
);

INSERT INTO public.point (geom) VALUES (
  ST_GeomFromText('POINT(0 51)', 26910)
);

INSERT INTO public.point (geom) VALUES (
  ST_GeomFromText('POINT(101 101)', 26910)
);

SELECT
  *
FROM public.checkpoint
  INNER JOIN public.point ON ST_DWithin(public.point.geom, public.checkpoint.geom, public.checkpoint.radio);