If TDS has been deducted than you should issue form 16. If there is no TDS deductions there is no need but even if you provide there should not be any problem
As employer you will be issuing only one TDS certificate. As employee if he has worked with more than one employer than he need to take and sumbit Form 16 from all the employers while filing the return. There is no other option.
if an assessee is employed under more than one employer during the year ,each of the employer shall issue part A of the certificate of Form 16 pertaining to the period for which such assessee was employed with each of the employers .Part B may be issued by each of the employers or the last employer at the option of the assessee