No caps, no punc, cannot read

His mistake, his responsibility.

You shouldn't be dragged into disputes between a contractor and sub-contractor.

If he paid less than expected, would he be sharing his windfall with you?

I would see if he would do it at cost and not add markup to it.  You paying the actual cost seems fair.

"i do understand contract is contract and mistake happens and offered him we can pay 1/3 of cost" OR...........

"in our contract our basement staircase was included to finish and its written clearly "

Both of these can't be true. It was in the contract to finished stair, or it was NOT?

Read the first six words, of the first line above. Buy your staircase, and next time? Really READ your contract.

Or....................

get with the "reliable/ trustworthy" contractor/ gc and work something out. Even I am not understanding the issue.

Ask him to do it at cost since it was his mistake. Yes I personally would pay for the mistake as mistakes happen but making a profit from it? Nope.

Maybe you need to be trustworthy and if you want a staircase then pay for it.

I think the other commenters' idea about offering to pay cost is a good one. One third isn't the contractor's cost, that's why he's balking. If the sub is doing all the work related to this line item then the contractor's cost could be 80% of what he's quoting you. Stair work is expensive and it's a specialty (when done right). It's very finicky and involves a lot of math. :-) Did he counter offer when you offered 1/3 or did he just dig in for full price?

Sorry but was this in or not in the contract ? That is where this ends . yes in the contract his dime not your dime wahtever you signed off on in the contract is what you get.

...since my partner and I have different opin[i]on it[']s quite hard to resolve ..

Try mediation. (Or marriage counseling.)

"in our contract our basement staircase was included to finish and its written clearly"

This statement is not clear. Please quote directly from the contract.

Is the current contract based on a "lump sum"? Is any of the work itemized?

Describe in detail the difference in the level of finish that is in dispute.

My contract specifies what is to be done including basement staircase

its not itemized per cost but its pretty black and white matter is is included in my contract

i will see if he will meet in half way or i will ask for trade work for my backsplash