how to trim existing stud width?
You have several options here, and you're going to be stuck with some limitations as to which method you use. You can use a reciprocating saw, but as it was pointed out by @JACK, there'e the danger of being unable to control the saw and cuttin all the way through to the other side.
You can use a hammer and chisel, but here you'll be shaking the entire wall and potentially cause some superficial damage that can cause some severe headaches if you have to match texture and/or paint. The reciprocating saw can also run this risk.
@Chris Butler also suggested a circular saw, which can work, but you're teetering on a very narrow edge and will cause a fair amount of mess.
My preference is to use a multitool if you have one available. If you don't have one, they're pretty inexpensive and very handy. This would allow you to do a plunge cut and you can use the fat edge of a speed square to help ensure you're keep to your 1/8&quot; or 1/4&quot; depth (1/8&quot; if trimming both studs or 1/4&quot; if only trimming 1 stud. These are also great in tight places.
You can try a combination of a laminate router, sharp utility knife, or chisel, but I wouldn't recommend that. I only mention it to try and cover all bases I can think of.
In case you have seen or heard of the multitool, here's a picture of one.