Why are bills that I paid to vendors showing up as deposits under reconciliations?

When you go into the Checking Register I'm assuming you do find a Deposit Transaction.  Double Click on the transaction (or Right Click and Edit) and look to see where the actual entry came from .  Is it as simple as you entered the amount in the wrong column when it was originally created? 

You can also go to the Vendor Center and look at all the transaction for the Vendor(s) that have the issue.  You should be able to trace it back to the original entry that has the issue.

Other possibility that is not common, but might have happened.  If you just Accept all the items that are brought down in the Bank Feed, sometimes they get miss labeled.  So are these "deposits" real deposits, but they say ABC Construction when they should be a Deposit from Customer A.

RE: When I go to Banking => Reconcile, on the right column that is labeled "Deposits" there are bills sent to me by vendors that have already been marked paid in quickbooks that are showing up as deposits.

This will happen if you use A/P and on the Bills you enter there you use the bank account as the expense account, or if you don't use A/P and just write checks, and on the checks you use the bank account as the expense account. Could that be what has happened?  If so, edit those transactions and use an appropriate account (probably an expense account) instead of the bank account.