Are children's finances considered when their father qualifies for Medicaid?

It sounds like you mean a long term care nursing home, not foster home. Your father's eligibility for  Medicaid for coverage of his long term care in a nursing home depends on his income and assets. If he has low enough income and few enough assets, Medicaid can cover the entire cost of his nursing home care for as long as he needs it. In determining how much income and assets he has, Medicaid will not consider your financial abilities or those of any other of his adult children.

However, you should be aware that if your father has given away any of his assets, or transferred them for less than full value, to his adult children within the five years before he applies for Medicaid coverage of nursing home care, those asset amounts might still count against his eligibility. If he made such a gift or transfer during that time, his Medicaid eligibility for nursing home coverage could be delayed. The length of the delay would be determined by dividing the amount of money (or value of the asset transferred) by the average monthly nursing facility cost in the state where your father lives. The number that results from this calculation is the number of months his eligibility would be delayed from the date he applies for Medicaid coverage.