It's kind of like regardless and irregardless. Both forms are found, and they mean the same thing, but only regardless is correct.
The correct form is sycophant, which is found in every major dictionary. Syncophant is only found in Wordnik, which only documents usage, not correctness. Also, "a sycophant" has 209K hits on Google; "a syncophant" has just 8K hits.
Bottom line: use sycophant.
Student or Learner