A Boolean-Phase swapping gate is introduced for quantum generality and cost-effectiveness, which is termed the “p-SWAP gate”, where p is a customizable phase difference for a set of swapped qubits and 0 <= p <= ({\pm \pi}) radians. The generality of the p-SWAP gate is proposed for quantum Phase oracles requiring a desirable p for a set of swapped qubits, as well as for quantum Boolean oracles when p is ignored. The cost-effectiveness of the p-SWAP gate comes from the lower quantum cost and depth for its final synthesized (transpiled) quantum circuit into a quantum computer, as compared to the standard SWAP gate. In general, the standard SWAP gate is constructed using three Feynman (CNOT) gates, while our p-SWAP gate only utilizes two CNOT gates. In this paper, the desirability of p is geometrically chosen using our proposed Bloch sphere approach, without using any matrices multiplication and unitary representations. After transpilation, the final transpiled p-SWAP gate has approximately 23% quantum cost reduction and 26% depth minimization than those of the final transpiled standard SWAP gate.