Short answer: Usually avoid raw banana during Paryushan if you are keeping the “no green vegetables (harit-shaak)” vow. Ripe banana (as a fruit) is generally allowed.

Details by tradition:

• Shwetambar practice: Many observe tyag of all green vegetables for the 8 days. Raw banana used as a sabzi is counted as “shaak,” so people normally avoid it. Ripe banana as a peeled fruit is acceptable. Also follow daylight eating and boiled/filtered water rules.
• Digambar practice: The emphasis is on ahimsa and personal vows; there isn’t a universal ban on all green vegetables for all 10 days. Raw banana is not a root (kand-mool), so it’s generally permissible unless you have taken a specific vow to avoid green vegetables; ripe banana is fine.

If you have taken stricter personal vows, follow those first. Always wash well, peel, and eat only in daylight.