Depending on model and yr, there may not be any mixture adjustment, most newer small engines only have fixed jets with nothing to adjust the mixture so there may or may not be a emissions limiter cap..
Either way, the fix is to remove and clean the jet and if equipped there is a tiny emulsion/mixing tube above the jet which has a bunch of little tiny holes.. It only takes one of those holes to plug to cause hunting..
If no tube then there may be a passage way past the jet clogged..
Not totally familiar with Onan carbs but have worked on a variety of small engine carbs from B&S, Honda and Honda clones and most of them use pretty much the same setup.