The short answer is: not so long as you stay current with your chapter 13 plan payments, assuming you are paying your regular mortgage payments through the plan.
Our U.S. Bankruptcy Court - Southern District of Texas Chapter 13 Trustee Procedures for Administration of Home Mortgage Payments provide that a mortgage company must apply the first payment that is paid them after the bankruptcy is filed, to the next payment due. So depending upon when they receive it, there could be one “post-petition” payment that is due but unpaid until the end of a chapter 13 plan.
In that case, there could be one late charge assessed, which the Trustee would pay. That is the only late fee that the mortgage company can assess during your plan, unless the mortgage company notifies the chapter 13 trustee in writing within 30 days of the date that a plan is confirmed that it waives all late charges that accrue after the order for relief in the case.
So long as a debtor remains current with Trustee payments (again, assuming that it is a "conduit" jurisdiction where the regular mortgage payments are paid through the plan), there should be no late fees. If a debtor is delinquent with Trustee payments, mortgage companies can charge late fees while a debtor is in chapter 13 and paying the mortgage through the trustee.
As a practical matter, most of the mortgage servicers will waive all late fees while a debtor is in bankruptcy. Also, at the end of the case, a Trustee will file a Motion to Deem Current, and the mortgage company must respond and indicate if they believe that the loan is current or not, and if not, how much and what for.
In most cases we get an Order Deeming Current at the end of the case, so the debtor's loan is considered 100% current and up to date, and the mortgage company cannot come back later and try to assess late fees that they say accrued during a chapter 13 plan.