"What happens to an employee's contributions when they're on paternity leave?"

Contributions can continue to be paid into the employee’s pension.

The employer should pay the contributions based on the employee’s pay before they went on paternity leave, while the employee should pay contributions based on the pay that they’re actually receiving (for example Statutory Paternity Pay).

So, the employee’s contribution might be nil if their earnings don’t exceed the lower earnings threshold if (for example) the qualifying earnings basis is being used.

Related: maternity leave and pension.