Graduity exemption

None. Of the amount will show in itr while filling 

And regarding form 16 it's given by his or her company and the value will be same as the company gives

Employer need to know which figures to be written in form 16 in exemption column

As per your saying
gratuity received 244000
gratuity eligible 350308
20 lakh as per amendment or 10 lakhs as per previous
which ever is less is taken
in your case 244000
now again exemption limit is 20 lakh as per amendment and 10 lakh as per previous
so fully exempted as per it return
if you're employer wants to show it in form 16 then add the least amount in salary
after that allowances exempted under section 10 deducut the same amount to get the gross salary

Which amount need to added in salary 244000 or 350308 because the balance 106308 received in current FY 20-21

The balance amount received of 106308  

Means what I can't understand you clearly 

See 26 as what amount they have shown you 

Upto 20 Lakh is exempt , balance is ready for tax