Can I appear for UPSC if I have a gap year or backlogs in college?

You can absolutely appear for the UPSC CSE regardless of gap years or a history of backlogs. The eligibility criteria focus purely on your final qualification. To apply, you only need to be a graduate from a recognised university; UPSC does not specify a minimum percentage or a "clean" academic record without failures.
As long as you have successfully cleared all backlogs and possess your final degree (or a provisional certificate) by the time you fill out the Detailed Application Form (DAF) for the Mains, you are fully eligible. The Commission views the exam as a fresh start, and your past academic struggles do not disqualify you from becoming an officer.
During the Personality Test (Interview), the board may ask about a significant gap or backlogs. However, they aren't looking for a perfect record; they value honesty and resilience. If you can explain how you used that time—whether for preparation, work, or personal growth—it often has no negative impact on your final score. Many successful candidates have overcome similar academic hurdles to secure top ranks.