When I was a kid I had a chart or book or something which actually listed the species in Yosemite by lake or stream, but I haven't seen it in 20+ years.
I don't know about White Wolf, but I've found that different waters in the park hold different species of trout. For example, May Lake and Tenaya Lake (like most of the high country lakes) has brookies, while Rogers Lake (a couple days hike north of Tuolumne) has rainbows.
I've caught brookies, browns, and rainbows out of the Tuolumne river, and brookies and rainbows out of the Merced river (in the high country, not the valley, where I've never fished), so offhand I would think you'd get at least brookies and rainbows out of any creek which holds fish up there.
Checking on TopoZone, the stream which flows through White Wolf campground is called the Middle Tuolumne River, which doesn't connect with the main Tuolumne River (which flows through Tuolumne Meadows) until outside the park (and below Hetch Hetchy). It's probably a pretty small stream, and fish will probably be 6 inches or smaller. At 7800 feet, all that's going to be there is trout.
Glancing at the White Wolf campground map that FishSteelhead linked to, the creeks are described as "seasonal", so I wouldn't expect much (if anything) in them.
You'll likely have to drive or hike to a bigger stream or a lake if you want to catch something. The Tuolumne River in Tuolumne Meadows has fish, Tenaya Lake has a few, May Lake (about a 2-mile uphill hike from the road) has a good population of brook trout. And the lakes (Tioga and Ellery) just outside the park's eastern boundary are stocked with rainbows.