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The topological phase transition and exotic quasiparticles in materials have attracted much attention because of their potential in spintronics and mimic of elementary particles. Especially, great research interest has been paid to search for the Weyl fermions in solid-state physics. By using first-principles calculations, we predict that the multinary semiconductor alloy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Tl</mi><msub><mi>Cd</mi><mn>2</mn></msub><msub><mi>Te</mi><mn>4</mn></msub></mrow></semantics></math></inline-formula> exhibits threefold fermions and nodal-line fermions, which are protected by the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mn>4</mn></msub></semantics></math></inline-formula> improper rotational symmetry. Moreover, owing to the lack of inversion and mirror symmetries, the threefold fermions split into Weyl fermions when the spin-orbit coupling is included. The chiral charge of Weyl points and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Z</mi><mn>2</mn></msub></semantics></math></inline-formula> time-reversal topological invariant are investigated. The topological surface states, spin texture, and electron-phonon coupling analysis are presented. Our study demonstrates <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Tl</mi><msub><mi>Cd</mi><mn>2</mn></msub><msub><mi>Te</mi><mn>4</mn></msub></mrow></semantics></math></inline-formula> as a good platform to understand topological phase transitions as well as possible coexistance of topological Weyl semimetal and superconductivity in one single material.