For your father to qualify for Medicaid, he needs to show that his income and assets are below the Medicaid eligibility levels in the state where he lives. This means providing income tax, bank and other financial accounts, and Social Security information, as well as documents about any assets he has. If you'll be gathering these documents for him, it may be helpful for him to execute a power of attorney for finances that appoints you as his agent. This could allow you access to his financial records and authorize you to deal directly with Medicaid eligibility officials. The power of attorney could be limited to the paperwork and time-span necessary to complete his Medicaid application, or it could be an open-ended authority to help him with his financial affairs. If the power of attorney is designated as "durable," it would permit you to manage his financial affairs if he becomes incapacitated.
Sometimes a Medicaid application requires proof of medical expenses. This might mean getting access to medical records that ordinarily are protected from anyone but the patient by the Health Insurance Portability and Accountability Act (HIPAA). If the Medicaid office requires that your father produce medical records and you need to help him gather them, your father can execute a HIPAA "release" of protected medical information giving you access to those records.