Can this be done?:

Assume C1 is in A1

If dragging A1 horizontally 1 cell over, the formula in B2: C2

If dragging A1 vertically, in A2: D1

Also inverse applying to the $ sign behavior.

C$1 will stay C$1 when dragged horizontally, but change the letter when dragged vertically.

$C1 will change the number when dragged horizontally, but won’t change letter when vertically.