A complete list of hotkeys for the original Heroes 3 does not exist; in fact, there are very many of them across various menus. The main hotkeys are listed in the manual for the original RoE game (ignore the link formatting): http://heroes3wog.net/download/[Heroes%203]%20Restoration%20of%20Erathia%20Manual.pdf
Hotkeys that seem to match those in the manual are also listed here: https://homm3sod.ru/keys/
For the HD mod, hotkeys are described on its website: https://sites.google.com/site/heroes3hd/rus/description/extended-ui
Specifically in HotA, the following hotkeys have been added:
Adventure Map:
— While holding Alt, you can see the path length (in movement units) of the current hero to different cells on the map (displayed in the bottom bar and via right-click).
— While holding Shift, you can select a hero by clicking on them on the map (instead of ordering another selected hero to go exchange with them).
Town Window:
— E — hotkey for exchanging between heroes.
Combat:
— G — hotkey for casting own spells for Faerie Dragons and area shots for Magogs, Liches, and Powerful Liches. The original F hotkey for faerie dragons is no longer active.
— Alt — hotkey to toggle stack action (melee attack/shooting, return/do not return after attack, attack/cast, move/cast).