Clock trees, which deliver the clock signal to every clock sink in the whole system, are one of the most active components on a chip which makes them one of the most dominant sources of noise. While many clock polarity assignment (PA) techniques were proposed to mitigate the clock noise, no attention has been paid to the PA under useful skew constraints. In this work, we show that the clock PA problem under useful skew constraints is intractable and propose a comprehensive and scalable clique search based algorithm to solve the problem effectively. In addition, we demonstrate the applicability of our solution by effectively extending it for PA under delay variation environment. Through experiments with ISPD'10 benchmark circuits, it is shown that our proposed clock PA algorithm is able to reduce the peak noise by 10.9% further over that of the conventional global skew bound constrained PA.