Hi Manoj,
Nearer to your first statement. Although, because this is a derivative, may be helpful to break into two pieces:
1. The 3-month period is “merely” part of the reference; the underlying is a 3-month interest rate.
2. The futures contract, in your example, is a one-year contract: bought on Jan 1st and settled (at maturity) on Jan 1st. Like any future, it “merely” refers to an underyling, in this case, the underlying is the 3 month interest rate that applies on the settlement day; i.e., the 3 month (spot) rate that applies if borrowing from Jan 1st to March 31st.
See how the futures contract (the derivative), in your example, has a one-year maturity and the underlying that is references has a three-month maturity (by design the maturity on the underlying rate “starts” when the futures settles)
Hope that helps (please no apologies about basic questions: it is what we do, I love the basics, they are constantly teaching me!)
David