Coherence and phase are the fundamental properties of light beams,and they affe ct each other.A new class of twisted Schell-model array correlated sources are introduced based on Mercer′s expansion.It turns out that such sources can be ex pressed as superposition of fully coherent Laguerre-Gaussian modes,and the twi s table condition is established.The mode decomposition theory used in this paper can be applied to the determination of any twisted beams with special correlati on structures.Furthermore,laser beams induce scintillations when propagating i n the turbulence.A tensor method is used to calculate the scintillations of a t wisted Gaussian Schell-model array beam in weak turbulence,analytical expressi o ns for the scintillation index are rigorously derived,and the influence of each initial optical parameter on the scintillations is detailed analyzed.The resul ts show that the scintillations can be reduced by increasing the beam waist widt hs,increasing the twisted factor and adjusting the Schell-model array correlat i on structure.It is interesting to impressing a twist phase on source beams can significantly inhibit scintillations effect.Our works are helpful to optimize t he overall performance of the partially coherent beam in atmospheric turbulent t ransmission,which may have potential application values in the fields of free s pace optical communication,lidar,and remote sensing imaging.