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The object of the present paper is to consider $f$-Kenmotsu $3$-manifolds fulfilling certain curvature conditions on $Q$-curvature tensor with the Schouten-van Kampen connection. Certain consequences of $Q$-curvature tensor on such manifolds bearing Ricci soliton in perspective of Schouten-van Kampen association are likewise displayed. In the last segment, examples are given.