I get social security income and I am on Medicaid, I have an option to start receiving part of my pension does this affect my Medicaid eligibility?

Learn the full specifics of the option for an early partial pension versus the option of waiting the maximum time for a later larger pension. Then, sit down with your caseworker and discuss both options on a face-to-face basis. After age 65, medicare and a larger pension may be better than medicaid and social security now. The safety nets for seniors are never large enough.

It's a math problem. If the minimum pension payment takes you over medicaid monthly income ceiling even with medical costs factored in, then it's not worth it.
You know this math quandary happens often for low wage workers. Like if they take the raise offered, it increases their income too much so they & their family fall off of medicaid or full copay under ACA rules so end up having to pay thier own premiums & full private pay dental. Financially it's better to stay part-time rather than be full-time; or be a $ 10/12 hr clerk rather than become a $ 16 hr supervisor as they have 2 kids who get all medical & dental covered with no copay if they stay low income. They can find they don't get subsidized housing or vouchers once income increases too. There are actually a lot of folks in this situation.

It might. You need to report the income to your caseworker. If your medical expenses are pretty high, you may still be Medicaid eligible.