Every state has down payment or homeownership assistance programs; some states have both. The programs are designed to provide affordable housing opportunities to homebuyers who might not ordinarily be able to afford a house.
Each program can have their own income and eligibility requirements but primarily the programs are available for first-time homebuyers or low-income families.
Keep in mind if you had no ownership in a principal residence in the previous 3 years, you are also considered a first-time homebuyer even if you owned a home prior to that 3-year period.
The programs are not usually administered directly through the State. Instead, they are nonprofit based and handled through a third party agency. The list below will start you on your search but be sure to confirm the program is currently available.
Department of Housing and Community Development
Programs by neighborhood – listing of neighborhoods