Is it possible to link a schedule C with a W2 reported on the 1040 income

You have a fallacy here: "A  self employed client that work in another State for about 3mos under a contract position, but took a W2, so he could record and pay the taxes."

You described a person that was able to be an independent contractor under certain circumstances and was Hired as an employee, instead. This is called Worker Classification. It could be that they would not have qualified to be independent under the employment conditions.

There is no such thing as "but took a W2." It's a Fact: either you are an employee or you are not. It could be that this employer knew better than to treat that as an independent contractor relationship; the IRS calls it Worker Misclassification. They see it a lot.

"While we record the w2 on line 1 of the 1040, we want to link his expenses to that w2 without recording the income on the two forms 1040/Sch C"

The W2 has nothing to do with any "side gig" or other business. None of the costs or mileage associated with that job are part of their own business, either. There are no Deductible Expenses for being someone else's employee.

You started another topic, here:

https://proconnect.intuit.com/community/proconnect-tax-discussions/discussion/re-can-my-client-deduct-hotel-rental-car-and-other-expenses-if/01/141436#M13714

Is that the same person as this topic?