The minimum you are legally required to pay during periods of sickness is Statutory Sick Pay (SSP). This is for any qualifying days if your employee earns enough to have this entitlement.
It makes no difference whether your employee is full- or part-time.
If your employee earns above the lower earnings limit, which currently stands at £118.00 per week (as of 2019), then they are eligible for SSP.
They will only be entitled to payment if they are ill for four or more days and will only receive SSP after three waiting days, these being days when your employee would normally work.
SSP is currently set at £94.25 (as of 2019) The amount you have to pay your employee for each qualifying sick day is calculated by dividing the weekly amount by the number of days a week your employee works.
Some employers will pay normal pay during the first three waiting days for statutory sick pay, but you are not required to do so.
You need to check your contract to see if you have any additional contractual obligations for payment during periods of sickness.