I habve been under a wage garnishment for the past year and a half. The total original amount on writ when it first started was as follows:

Original amount owed $7366.20
Plus interst due on Judgement 4319.56
Taxable Costs 110.00
Principal balance/Total amount due and owing
$11,795,70

I have paid from wages reducing 696.00

But the law firm says that I owe interest that has been accumulating and cost of 2 additional writs updating what I owe over 1300.00 more

My question is once a writ is served to garnish wages filed in court can they add interest and cost of updating writs on what I owe that was never sent to me?

This will depend on where it is and the terms of the judgement, so in some places yes, have you read the actual judgement. The garnishment is merely collection of the judgement, so you have to go back to see what the judgement is for