How to smoke SKINLESS chicken leg quarters

Absolutely nothing to worry about.  Leg quarters are dark meat.  Dark meat has more fat than the white meat.  I smoke or grill/smoke boneless, skinless thighs all the time.  They can handle about any temp.  I usually do them hot n fast on my WSM to an IT of 165-175F.  Leg quarters are no different.

In my Weber Kettle, I use a paella pan with a cooling rack inside it, putting the seasoned chicken thighs on the rack.  I position two charcoal baskets in the center of my grill on the charcoal grate and put a chunk of hickory in each basket.  Then I fire up a half chimney of hot coals and evenly distribute them in the baskets.  Replace the cooking grate, put the paella pan right over the baskets, put the lid on the grill then grill/smoke them until they reach 165 to 175F.  I don't bother waiting for TBS and they never taste ashy because the coals are so hot.  Chamber temp can get up into the 400s at times, but is usually in the 350F range.  Depending on the size of the thighs, or in your case leg quarters, they are usually at the right IT in 30-45 minutes. 

Sometimes I sauce them, but not often.