We present a reduced-cost implementation of the IP-EOM-CCSD* method using statespecific frozen natural orbital and density fitting approximation. The state-specific natural orbitals are calculated using the IP-ADC (2) method. The use of truncated state-specific natural orbital significantly reduces the size of the virtual space and speeds up the calculations. The accuracy of the method can be systematically controllable using natural occupation based truncation criteria, and a threshold of 10 -4. gives the best compromise between accuracy and computational cost. The state-specific natural orbital offers an advantage over the standard MP2 natural orbital method that the error can be reduced through a perturbative correction in the former. This reduction in error allows for the use of a lower occupation threshold, ultimately decreasing the computational cost. The computational cost of density fitting can be further reduced by using truncated natural auxiliary functions. Truncation of the auxiliary basis functions with a natural auxiliary threshold of 10 -2 will give almost identical results as that of the untruncated result. The use of CVS approximation in the triples part and the frozen core approximation leads to small errors. The use of partial triples correction greatly improved the agreement with the experiment compared to the standard FNO-based EOM-CCSD methods. It is observed that for second-row elements, the error resulting from neglecting relativistic corrections partially offsets the error arising from the absence of higher-order correlation corrections. The accuracy of the method has been benchmarked on a large test set containing 176 experimental K-edge core ionization energies. Using the SS-FNO-IP-EOM-CCSD* method provides significantly higher accuracy compared to the previously implemented IP-EOM-DLPNO-CCSD method , even when using a tighter truncation threshold for the latter. The SS-FNO-IP-EOM-CCSD* method can be combined with projection based embedding scheme, which allows one to truncate the occupied space in addition to virtual space truncation achieved by SS-FNO approximation. The efficiency of the present implementation has been demonstrated by calculating the core-ionization energies of a molecule containing 60 atoms and more than two thousand basis functions. The impact of relativistic effects on the ionization energy of second-row elements at the K-edge is minimal, and scalar relativistic effects are typically satisfactory . However, when studying heavier elements, higher-level relativistic effects must be taken into account. To accurately simulate the core ionization energies of molecules with heavy elements, a cost-effective approach such as the natural spinor-based IP-EOM-CCSD* method, which incorporates a four-component relativistic Hamiltonian and higher order relativistic corrections, is necessary. Work is in progress towards that direction.