No. Father's Day is not a federal holiday in the US, so government offices, banks and schools follow their normal schedule unless they choose otherwise.
When is Father's Day 2097?
Father's Day 2097 falls on Sunday, June 16.
Why does the date of Father's Day change each year?
It is set by a rule rather than a fixed date: third Sunday of June. The day of the month moves each year to keep that weekday.