Please keep in mind that anytime you see the Denied status on a claim, this is being sent directly from the insurance payer.
It is important to note that some payers will choose to send the Denied status when a claim goes towards a client's deductible. This is because they are technically denying payment to the provider and putting the financial obligation on the client. However, this will vary across payers and you may see that others choose to distinguish between this type of claim and will send the Deductible status.
In either case, if you'd like a claim that went toward a client's deductible to be marked as Paid after the client has paid their portion of the session fee, you can do so by adding a manual insurance payment for $0. You will simply want to allocate the $0 payment to the appropriate session(s) and adjust the write-off for each DOS on the claim to update the claim's status to "Paid.
Tip: Here's a quick guide that goes into detail on how to do this: How do I bill clients who haven't met their deductible?