The Stairs Going To My Basement Are 36 inches Wide.. The Stringers Are Cut out... I Want To Finish The Job.. I Am going To Put On New Threads & Kick Board.. The Problem Is If It is a Problem, There Is No Room To put A Cover Board On Each Side.. I Ran A Wall On Each Side Of The Steps & There Is 37 inches Wall To Wall ,The Steps Are 36 Inches ,So I Have Room For Half Inch Drywall On Each Side.. So I Will Have To Put The Threads Tight Against The Drywall.Will It Be OK If I Screw The Stringers To The Wall & Run A 2x4 Underneath The Stringer For Support.. Would That Be OK & Cut Down On Movement & Not Rub The Drywall?. I Can Also Support The Stringer Underneath With A Couple Of Vertical Studs.. If The Cover Boards Must Go There I Would Have To Make The Steps More Narrow & I Rather Not Do That Only If I Have To.. Please Explain Where I Am Standing & My Options.. Thanking U In Advance. (I Cannot Make The Walls Wider, No Room For That.. 37 Inch Wall To Wall Is Max ).Waiting For Some Good Information.. Thanks Again.

Attaching the stringers to the stud walls will make the stringers sufficiently strong without the cover boards.. Especially with the 2x4 underneath them. However that will make finishing of the drywall difficult and make painting, now and in the future, tedious.
May I ask why you don't simply cut the length of treads and risers to fit the space you have?