Just because it can be useful for other people, I post here the simple solution I found after looking for some time in the documentation, as suggested by cfort:
ax.xaxis.set_ticks_position('both')
ax.xaxis.set_tick_params(direction='in', which='both', labelsize=16)
ax.yaxis.set_ticks_position('both')
ax.yaxis.set_tick_params(direction='in', which='both', labelsize=16)
ax.minorticks_on()
these lines of code set the tick inwards on both sides (e.g. for the x axis they are placed at top and bottom of the figure), set the label size and add the minorticks, which will point in the inward direction as well.