Abstract
This paper discusses on the estimation of character sums with respect to non-homogeneous Beatty sequences, ⌊𝜶𝒑+𝜷⌋ over prime 𝒑≤𝒎 where 𝜷∈ℝ, 𝒙∈ℕ and 𝜶>𝟎 is irrational. In particular, the bounds is found by extending several properties of character sums associated with composite moduli over prime. As a result, the bound of 𝝋(𝒎)𝟏𝟒#𝓟𝟏𝟐+#𝓟𝑫𝜶,𝜷(𝑷) is deduced.
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