Very unlikely. Jats are probably of local indian or indus valley origin.
The only jutes who probably came to india are the English colonisers of 19th century and the only Jats to reach England are probably the recent immigrants.
Not even that connection is likely with Jutland.
As for mitochondrial Dna and y chromosome, we still dont have that much data and a lot of it is conflicting. More analysis is needed - and quickly before interbreeding destroys even that.
Any 2 populations living in proximity soon exchanges a lot of genetic materials even within 100 years leave alone 3000 years