I'm trying to make a Hero Core clone for the TI series. The original game has 8*8 sprites and tiles and the playfield measures 20*20 tiles. The TI-84 however has the capability to draw 96 8*8 tiles or 384 4*4 tiles which comes close to the original max of 20*20=400 tiles. Is it better to use 4*4 tiles and have more room to play with or plain 8*8. Scrolling is no option, because the original game has no scrolling at all.

4*4 is usually better for action games, particularly when there is no scrolling.

Lol even those graphics are hard to port to the crappy 96*64 screen of the TI84. 4*4 it will be. The sprites are going to be 4*4 too I guess. It looses the whole graphic dimension by doing this But the gameplay will be quite the same as the pc version. Bosses and some enemies will have bigger sprites. Are there 4*4 sprite drawing routines? Not the type of fake sprites axe uses now. I mean real sprites that replace a part of the tiles and when they move along the tiles only have to be redrawn in that certain area. This will speed up games dramatically I guess.

There are no 4x4 sprite drawing routines in axe. But you can use the the standard 16 digit hex code and just keep the the rest 0.
Drawing can be managed if you multiply the x and y of the Pnt-On()-command in your for loop by 4 instead of 8.

That's what I would do as well, multiplying the x and y by 4 instead of 8. Unless there's a faster way.