The TI-99/4A makes use of different kinds of storage media, which are also represented in MAME.
The read-only memory used in the TI console or in other members of the TI family are mask ROMs / EPROMs, or GROMs, a special kind of 8-bit streaming ROM with 6 KiB capacity. To be used in MAME, the contents of the ROM chips must be put into a file ("ROM dump"), and this file must then be stored in a ZIP container and put into a directory that is located in the "ROM path".
Peripheral device ROMs
Also called cartridges, with ROM, RAM, or NVRAM
This is probably a bit misleading, because MAME does, in fact, not support accessing single files. I thought it would be better to mention it so that you don't have to guess whether it works or not.