HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

ilushka, in the main window of the HD mod, there are several options in the upper right corner that allow you to customize the game to your liking: resolution, renderer, and stretch filter.

Changing the resolution in the game changes the size of the visible area of the map in the adventure window and when viewing the world/land/air.
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In the HD launcher (HD3_Launcher.exe), you can choose one of 4 color modes: ...

Read more here.
To avoid black bars on the edges, set the resolution to be equal to or a multiple of the number of pixels in your monitor's current mode (if in windowed mode) or equal to the maximum physical resolution of the monitor (if it is an LCD).