We study T-quasigroups with Schr¨oder identity xy · yx = y [1, 2, 3]. Definition. Quasigroup (Q, ·) is a T-quasigroup if and only if there exists an abelian group (Q, +), its automorphisms φ and ψ and a fixed element a ∈ Q such that x · y = φx + ψy + a for all x, y ∈ Q [4]. A T-quasigroup with the additional condition φψ = ψφ is medial. Theorem. In T-quasigroup (Q, ·) of the form x · y = φx + ψy Schr¨oder identity is true if and only if φ2 + ψ2 = 0, φψ + ψφ = ε. Corollary. In medial quasigroup (Q, ·) of the form x·y = φx+ψy Schr¨oder identity is true if and only if φ2 + ψ2 = 0, 2φψ = ε.Example 1. Suppose we have the group Zn of residues modulo n. If φ = 3, ψ = 1 then φ2 +ψ2 = 9+1 = 0 (mod 5),n = 5. Further 2φψ = 2· 3 ·1 = 6 = ε = 1 (mod 5), x · y = 3x + y (mod 5). Check. 3(3x + 1y) + 1(3y + x) = y (mod 5), 9x + 3y + 3y + x = y (mod 5), y = y (mod 5). Example 2. Suppose we have the group Zn of residues modulo n. If φ = 10, ψ = 2 then φ2+ψ2 = 100+4 = 104 = 0 (mod 13),n = 13. Further 2φψ = 2 · 10 · 2 = 40 = ε = 1 (mod 13), x · y = 10x + 2y (mod 13). Check. 10(10x+2y)+2(10y +2x) = y (mod 13), 100x+ 20y + 20y + 4x = y (mod 13), y = y (mod 13). Example 3. We construct quasigroup x ◦ y = 2657x + 7063y mod (9721) and check that in this quasigroup 3-rd Stein identity is fulfillment : 2657(2657x + 7063y) + 7063(2657y + 7063x) = y mod (9721), 7059649x+8766391y+8766391y+9885969x = y mod (9721), 56945618x+37532782y = y mod (9721), y = y mod (9721).