In the framework of the Jacobi-weighted Sobolev space, we design the a-posterior error estimators and error indicators associated with residuals and jumps of normal derivatives on internal edges with appropriate Jacobi weights for the p-version of the finite element method. With the help of quasi Jacobi projection operators, the upper bounds and the lower bounds of indicators and estimators are analyzed, which shows that such a-posteriori error estimation is quasi optimal. The indicators and estimators are computed for some model problems and programmed in C++. The numerical results show the reliability of our indicators and estimators.