Short answer: Yes — FitsAir does offer web/online check‑in according to its own website. (fitsair.com)

Details and caveat:

• FitsAir’s site has a Web Check‑in / Manage Booking section where you can complete online check‑in. (fitsair.com)
• Several booking sites list a typical web check‑in window (for example, opening ~48 hours before departure and closing a few hours before), but exact times can vary by route and ticket. Verify the exact opening/closing times for your flight on FitsAir’s site or your booking confirmation. (makemytrip.com)
• A few third‑party summaries conflict and state airport‑only check‑in for some routes, so if you can’t find the web check‑in for your reservation, contact FitsAir to confirm. (alternativeairlines.com)

If you want to proceed now:

• Go to FitsAir’s Web Check‑in / Manage Booking on their website. (fitsair.com)
• Or contact FitsAir customer service: +94 117 940 940 or [email protected] for definitive confirmation for your specific flight. (fitsair.com)

If you’d like, tell me your flight route or booking reference and I can help check the specific check‑in options (I’ll look it up).