In Jain tradition, the 2 Oli observed in a year are:

1. Chaitra Oli — in the month of Chaitra
2. Ashwin Oli — in the month of Ashwin

These are also called Ayambil Oli, and they are periods of special fasting and spiritual साधना dedicated to Shri Shatrunjay and Navpadji worship in many traditions.

If you want, I can also explain the meaning of Oli and the rules of Ayambil in simple words.