Susie,
Unfortunately, birth records recorded in Ukmerge are sparse. There is 1895, which has been indexed, and then 1922-1939, which have not been indexed yet because of 100-year privacy. That's it, unless something new turns up somewhere. If you are seeing birth records for other years (e.g. 1914) they may mention Ukmerge as, for example, the father's place of origin, but they are not Ukmerge births and would have been recorded somewhere else.
Russ Maurer
Records Acquisition & Translation Coordinator, LitvakSIG