Yes my sample collection is very slow. My supervisor is very paranoid when it comes to collaboration or collecting samples from other hospitals since he's afraid they would demand co-authorship or steal his research. Even I'm not allowed to reveal certain aspect of this research to the person who is complete stranger such as biostatistians who are not from our universities. It's very difficult to persuade him to collect sample/ ask for advice in statistics as I already asked for his view on the matters mentioned.

I am very stressful now. My sample collection won't meet the target set by my supervisor if I were to collect samples for 1 and a half year only. Based on my calculation, I will only meet the demand set by my supervisor if I collected the samples in 3 years which is not going to happen since I am on scholarship and I need to graduate on time. My supervisor is blaming me now for sample collection and nothing further I can do until he agrees to collect samples from other hospitals.

That sounds indeed really stressful. And your supervisor does not seem to have realistic expectations. You just cannot collect samples faster if there are none available locally that fit your criteria!

Is there any way to prove to him that you just can't get more without external samples? I am thinking along the lines of maybe a hospital database of registered patients and how many have the characteristics you select by. I assume you do not have direct access to patient data in any case, but you could find out who handles this in your department and ask them if they could help you with an anonymised statistic. For my project, I have such a list of all the cases admitted here since a certain year which fit my criteria.
Not sure if that is applicable in your case, but something similar could help you convince your supervisor that his expectations are impossible. He either has to budge on the external sources or has to accept that your sample size will be much smaller.