Regardless of whether your father is truly head of household, you can apply for food stamps yourself and the intake worker will ensure your application determines if you are eligible, and act accordingly. However, if you falsely claim your father to be head of household, you can land yourself in a bit of legal trouble, including welfare fraud and theft against the state, which may end up in a conviction and incarceration. Just be very sure to answer the questions accurately so you don't find yourself on the wrong end of the law on this.
I am assuming he is ineligible due to citizenship/residency ruled. You apply, list your father on the application. His income counts on the case . My suggestion is apply, be honest,and work with the eligibility worker.
This is for general information only. Nothing in this information should be construed as creating an attorney-client relationship nor shall any of this information be construed as providing legal advice. Laws change over time and differ from state to state. These answers are based on California Law.Applicability of the legal principles discussed may differ substantially in individual situations. You should not act upon the information presented herein without consulting an attorney about your particular situation. No attorney-client relationship is established.