As an EEE (Electrical and Electronics Engineering) graduate, your core GATE paper is EE (Electrical Engineering).
You can also choose papers like IN (Instrumentation) or EC (Electronics and Communication) if you're comfortable. GATE now allows two-paper combinations EE plus IN is a valid pair.
Choose based on your strengths and future goals (e.g., PSU jobs, M.Tech). Always check the latest GATE brochure for updated paper codes and combinations.