In Jain dharma, the word you are asking about is most likely “tāpsī / tāpasi / tapasvī” (often spoken as “taapsi”).

Meaning in simple words:

• Tapas / Taap (तप) = austerity, penance, doing taap for destroying karma (like upvas, ekasana, aayambil, varshitap, etc.).
• Tapasvī / Tāpsī (तपस्वी / तापसी) =

A person who does regular, sincere taap (austerities) for atma-shuddhi (soul purification) and moksha-marg. In short: “Je vyakti jatan thi tap kare, ene tapasvī / taapsi kahe.”

It is not a separate ritual or special fast; it is simply a name for the practitioner who performs taap correctly, with:

• right faith (samyak darshan),
• right knowledge (samyak jnān),
• right conduct (samyak chāritra).

Both Digambar and Shvetambar traditions use the same basic sense: “Tap karnaar sādhu-sādhvī athvā shrāvak-shrāvikā” = tapasvī / taapsi.

If you meant something more specific (like a name of a particular tap), then it is likely a local or colloquial usage; in classical Jain shastra “taapsi” mainly means a practitioner of tapas.