My question is in regards to obtaining the yield of a specific tenor at any date (for example, when constructing the yield curve). For example, when calculating the yield for a specific zero-coupon (zc) bond with the tenor (i.e. time to maturity) of 3 months, one has multiple options: the 3-month on the run zc bonds, all the longer maturity zc bonds with the time-to-maturity of 3 months (i.e. bonds with 6M, 1y, ... maturity).
My question is whether there is some kind of averaging of the yields of all these bonds which have the same tenor but different maturities? In theory, with a fixed par value, the price of a 1y zc bond with 3 month to maturity should be the same as the price of a 3M zc bond in the secondary market.