In STM32F303RE my customer is trying to use 3 timers but problem is happening with using them at the same time as it is real time application

Increase the stack size maybe?

I assume that all interrupt service routine can coexist, clear the pending interrupt and have been put on same priority level and they don't use HAL_Delay() within them

All these for sanity check

You mean HAL_Delay(); in interrupt handler?

Interrupt handler should be as brief as possible and only manage what is critical, so so printf, no delays.

The embedded MCU art is to well understand all the interrupt max latency and duration and make sure there is no weak race condition which could occur once overnight. Usually there is no tool for this kind of profiling and this is what is the trickiest to manage.

Anyway, I really feel you should check what is the stack size used in the project.

Pretty sure the HW works correctly. More probable you have some blocking or deadlocking issue on the SW side.

Debug the hardfault, track back from the stack content and the fault registers, where did the fault happen.

The technique to do this has been discussed here many times, search perhaps for "hardfault handler" in Clive's posts.

JW

Hardfault indicates a software problem, most likely uninitialized, corrupted or otherwise improperly used pointers, maybe stack overflow.

You have the code, we don't. How could we guess?