When the Supplemental Security Insurance (SSI) program looks at someone's eligibility, and at how much monthly SSI benefits someone receives once they qualify, they take into account that person's income
and assets. However, they do NOT count the income earned by an adult son or daughter (unless that money is paid directly to the parent). So, the income you would earn from taking a job would not directly affect your father's SSI eligibility or payment.
However, what you do with the money you earn might affect his SSI eligibility or benefits. If you regularly spend some of the money you earn on food or clothing for your father, or if you spend it on his housing costs, SSI could take those amounts into consideration as "income" to your father. This would only be the case if you spent this money on him regularly -- occasionally buying food or a meal out would not matter.