In　this　paper,　we　study　the　tests　for　sphericity　and　identity　of　covariance　matrices　in　time-varying　coefficient　high-dimensional　panel　data　models　with　fixed　effects.　In　order　to　construct　the　effective　test　statistics　and　avoid　the　influence　of　the　unknown　fixed　effects,　we　apply　the　difference　method　to　eliminate　the　dependence　of　the　residual　sample,　and　further　construct　test　statistics　using　the　trace　estimators　of　the　covariance　matrices.　For　the　estimators　of　the　coefficient　functions,　we　use　the　local　linear　dummy　variable　method.　Under　some　regularity　conditions,　we　study　the　asymptotic　property　of　the　estimators　and　establish　the　asymptotic　distributions　of　our　proposed　test　statistics　without　specifying　an　explicit　relationship　between　the　cross-sectional　and　the　time　series　dimensions.　We　further　show　that　the　test　statistics　are　asymptotic　distribution-free.　Subsequently　simulation　studies　are　carried　out　to　evaluate　our　proposed　methods.　In　order　to　assess　the　performance　of　our　proposed　test　method,　we　compare　with　the　existing　test　methods　in　panel　data　linear　models　with　fixed　effects.