  We give an obstruction for genus one knots $K$, $K'$ to have the Gordian
distance one by using the $0$th coefficient of the HOMFLT polynomials. As an
application, we give a new constraint for genus one knot to admit a
(generalized) cosmetic crossing. Combining known results, we prove the
(generalized) cosmetic crossing conjecture for genus one pretzel knots.
