ModelSim executable not found in C:/intelFPGA_lite/simulation/modelsim Error.

The directory should be qsim (for Questasim), not modelsim, just as shown in the window. Questasim replaced Modelsim in Quartus about 2 or 3 years ago, so if you're using 23.1, it should be qsim or questasim in the path, not modelsim.

I have attempted to run the simulation the following ways and I am still receiving an error message. Can you explain further what you mean since there is still a persisting error?

You may take a look at below forum as I believe this is how you should specify the path.

https://community.intel.com/t5/Intel-FPGA-Software-Installation/How-to-specify-a-path-to-the-executables-of-the-ModelSim-Altera/m-p/649061

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I just make an account just to share this 
randomly found it 
even though it has been 2 years i think that you've already found the solution
install modelsim and make this folder as the directory modelsim_ase\win32aloem