Your circumstances are not very clear at all.
I was on student visa .
When did or does this visa expire?
Now I was on fee waiver application . 2 days before fee waiver application has been rejected by home office .
What do you mean? Did you apply for another visa or what exactly did you do and what was refused?
So I want to switch my visa asap.
What visa do you currently hold exactly?
3 months back I applied for tyre 2 sponsorship visa .
Did you apply for a VISA or for a JOB with an employer to sponsor you for a Skilled Worker visa?
But so far they have not provided cos.
You need a CoS to apply for a Skilled Worker visa. A CoS is also only valid for 3 months to enable you to apply for the visa. If you do not apply, the CoS becomes invalid.
Because of my urgency they say go for fingerprints and will do ur application on cos reference number.
What urgency exactly? You have not explained your situation very well at all. What CoS reference number is this and where and when did you get it?
When cos comes will submit your cos in home office.
You need the CoS to apply for a visa.