This thread on forum.mflenses.com concerns the same issue, and seems to answer the question.
Poster SonicScot has the same problem and shows how it is caused by the focus ring extending further than the inner ring on the lens, which is supposed to touch the adapter.
Clearly the focus ring is in the way of the adapter. I'd like to know if there's a way of moving it.
According to other posters in this thread, this is an issue with some Helios 44-3 lenses. As a result, you are only tightening and loosening the lens from the adapter when rotating the focus ring.
Poster alex1967 suggests buying a more expensive adapter like the Rayqual M42 to Canon EOS adapter.
Save some money and invest to high quality Rayqual and eliminate the problem. My Helios 44-3, S/N ******* works just fine, but will have the same issue as discussed above with cheap adapter.
Images of that adapter shows it has a hollow front end as opposed to flat on other widely available adapters. Perhaps that will be enough to fit the additional length of the focus ring. However, there is no confirmation that this adapter will work on all Helios 44-3 models and the Rayqual adapter is quite expensive. I have found one cheaper adapter type on eBay that has a similar hollow front end, but the hollowness stop a bit further from the edge. Comparing these images with where the focus ring touches the adapter I already have, it's difficult to tell whether either of these adapters will work. It would be a tight fit.
Poster hpmickey refers to this post on pentaxforums.com, suggesting to sand the additional length of the focus ring. That suggestion seems like it would work, but requires making alterations to the focus ring.
Update
The cheaper adapter did not work. I misread the picture. It doesn't provide any more room than the other cheap adapters.
(Helios on left, Takumar on right)
