3% down conventional is not one program.
Fannie Mae and Freddie Mac each have multiple 97% LTV pathways. Choosing the right one depends on first-time-buyer status, income, property and other eligibility rules—not simply the down payment.
Fannie Mae
Fannie offers eligible 97% LTV purchase executions through its standard 97% option and HomeReady. The exact first-time-buyer, income and transaction requirements depend on the path used.
Freddie Mac
Freddie offers HomeOne and Home Possible 97% LTV pathways. HomeOne is designed around eligible first-time-homebuyer purchase transactions, while Home Possible is its income-limited affordable offering.
Official sources
Fannie Mae Selling Guide · Freddie Mac Seller/Servicer Guide · FHFA Conforming Loan Limits
Agency guides control over summaries. Lender and mortgage-insurer overlays can be more restrictive.