Obtaining power spectral density without having knowledge about frequency bandwidth or sampling frequency of the signal in Matlab?
Without more information about the signal, it is not possible.

The set of samples is just a set of numbers with no further information associated with them. If you know the frequency at which the samples were taken, then you can associate "real-world" frequencies to their FFT bins. Otherwise, it may be impossible.

To give an example, consider the samples of $\cos(2\pi 100t)$ taken at $f_s=500\,\text{Hz}$, and the samples of $\cos(2\pi 200t)$ taken at $f_s=1000\,\text{Hz}$. They are exactly the same! There is no way to tell the two signals apart just from their samples.

It may be, however, that you have some extra piece of information that may help deduce $f_s$. For example, you may know that the signal's spectrum has a peak, or a particular phase, or some other property at a certain frequency. If you find the normalized FFT of the samples and identify this property, you can extrapolate from there to estimate the actual signal frequencies.