4th time out in a half
 

We did an 8th grade game today and team A called a time out late in the 4th quarter but were out of timeouts. Our white hat called an unsportsmanlike then granted the timeout. Is this correct?

NO.
First of all the request should be denied. All officials should know the TO status especially when a team has expended them already.

Once it was discovered you allowed the 4th TO, shoo them off the field and restart the clock and blow the RFP.
No foul should be assessed.

Your WH must have been trying to liken Football to Basketball. I agree with Theisey, NO Foul, do not grant the TO, and if you do stop it as soon as you realize they don't have any, get the clock running and coaches/water off the field.

Officials must know who has what timeouts left. If they are out of timeouts, do not grant their request.

Ignore it
 

This is not basketball where you can "buy" a TO with a technical. During the third TO, remind each other that they must ignore any requests for a TO by that team.