Short answer:

• There is a special ritual during Paryushan called Mahavir Janma Vanchan. It is not the actual birth anniversary (Mahavir Jayanti) itself, but a narration about Mahavir’s birth and Mata Trishla’s 14 dreams that is read on a specific day of Paryushan.
• The true Mahavir Jayanti (birth anniversary) is celebrated in different months depending on tradition: Śvetāmbaras usually in Chaitra, while Digambar texts place Mahavira’s birth in a different historical period. Because of these differences, some communities connect the Mahavir birth story with Paryushan through Janma Vanchan, while others keep the two occasions separate.

What this means in practice:

• On the 5th day of Paryushan Parva, Jains may listen to or recite the Mahavir Janma Vanchan, which recounts Mata Trishla’s 14 dreams and Mahavir’s birth. This keeps Mahavira’s teachings and spirit visible during the purification and forgiveness focus of Paryushan.
• The actual Mahavir Jayanti—the birth anniversary of Mahavira—remains a separate festival in the Jain calendar for those traditions that observe it (often in Chaitra for Śvetāmbaras).

You can read more about how Mahavir Janma Vanchan fits into Paryushan in Jain traditions here