Fundamental properties of finite two-dimensional (2D) Yukawa dust clusters, subjected to power law confining potentials, are studied using Monte Carlo simulations. We show the effects of the interplay between the Yukawa screening and the functional form of the confining potential on the structure, dynamics, and melting of few particle systems. We find numerically that one of the fundamental eigenmodes, namely, a center of mass mode, still exists for a confinement with n = 3. The stability of such clusters is discussed using the variance of the block averaged interparticle distance fluctuations (VIDF). The melting temperatures are found to depend crucially on screening length and confinement power. For the estimation of the melting temperature, the VIDF quantity is believed to be reliable only for well-packed structures, where the relative interparticle distance fluctuations (IDF) disregard the melting transition point.