I want a white filling inside the black dot
Graphics[{Black, FillingStyle -> White, PointSize[0.035], Point[{1, 2}]}]
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doesn't have a distinction of interior and edge. Use Disk
instead:
Graphics[
{EdgeForm[Black], FaceForm[White], Disk[{1, 2}, Scaled[0.035]]}
]
Use a Disk instead of a Point.
Graphics[{EdgeForm[{Thick, Black}], FaceForm[White], Disk[{1, 2}, 0.035]},
PlotRange -> {{0, 2}, {1, 3}}]