If you’d like to see some government usage, take a look at the US Mint site, which they call 250 years semiquincentennial. If you remember bicentennial coins, you’ll probably also see semiquincentennial coins.
Semiquincentennial, Bisesquicentennial, Sestercentennial, Quarter Millennial — good to know because this year on 10 November will be the Marine Corps’ 250th birthday. Although I don’t think I’ll use any of those terms. It’ll simply be USMC 250.
When my home town celebrated its 150th anniversary, they called it the sesquicentennial, but that’s off by a century from the question posed by the OP.