PHD Part Time vs Full TIme Will it make any difference if you do a PHD full time or part time ?

In my case my diploma/certificate will mention that the PHD was done part-time, how will this affect my career afterwards? will it have any implications on an academic career ?

The reason for which i have to complete my part-time PHD in 3 years is that i am working at the same university, and my job is actually a researcher on the exact same topic of my PHD. I was initially registered as part-time due to the nature of my situation, but apparently i can change that in to full time, however i want to see if it will be worth the struggle.
I find it unfair that i get the PART-TIME on my diploma although i did in 3 years as any other Full time PHD

Also, i would like to mention that in my case, a part time PHD will also have to be completed in 3 years*, same as the full time PHD.

Lets assume money is out of the question in this case
I will give two answers, you are welcome to choose which one to pay attention to ;)

Short answer: If you can change to full time without negative consequences, then I don't see why not. It might look a little 'cleaner' on the diploma and might prevent some biases or questions that part-time doctoral work might arouse in your country (assuming you want to remain in your country, here you are a better judge, since our countries are probably not the same as 3-yr PhDs are definitely not the norm in the U.S.). So if the benefits outweigh the effort, go for it!

Long answer: I realize everyone's circumstances are different and there may be reasons to rush a PhD for the sake of the diploma and a brighter future with higher salary. With this disclaimer, to me, any (part or full time) PhD done in 3 years by design of the program (rather than special case as with some highly talented students) raises suspicion about the quality of the PhD program.  However, from your comment it sounds like it's not that the program is designed to be have 3 year typical duration; it's that you have 3 years of funding on your job contract. That changes the situation, because it means that you are potentially rushing like crazy through a PhD program that is intended for a longer average completion period (e.g. 4-5 years). 

This is important because regardless of what your transcript will say, it's what is left in your head that will ultimately determine your worth as a professional in your field. 

Students who complete a PhD in 3 years are either highly talented and do so with no detriment to their knowledge - to say it different, they complete the PhD in 3 years because when they are done, their knowledge is at least equivalent to that of typical students who take longer. They are ahead from the start, hence the typical program is too slow for them. That's an OK situation. Different strokes for different folks.

Another situation is that students who complete a PhD in 3 years are in a big rush, the reason being that there are strings attached, and a longer term carries a higher cost either in money, or time (e.g. fellowships that require a student to return for home country for a minimum of 2x the duration of PhD study). 

This is problematic for the obvious reason that simply being in a hurry does not make one more qualified by the end of the 3rd year, i.e. more ready to graduate. The reason why this is problematic is the same as the reason why it is problematic if a medical student completes medical school in 2.5 years instead of the typical 5, or an attorney graduates from law school in 1.5 years instead of typical 3. Even if you study really hard, it raises eyebrows. To me personally, a PhD completed in 3 years raises eyebrows in the same way.

I offer this as something to think about because being in a hurry seems to be at least partly the case here. If I am wrong, please correct me. I might also be biased by my own graduate study, which I did not rush. As a result it took longer than average, but I did not see it as a race, and I honestly believe that I have gained more skills, knowledge and experience (and perhaps a little wisdom) than if I had rushed it. 

Bottom line: If at all possible, I recommend to reconsider your plans, taking into account factors other than the contract duration of your job. So far it seems that this single factor is the main consideration. The assumption is that once 3 years is up, that's it, life is over, there is no money left in the universe to fund your study. Is that truly the case? Could it be possible to find fellowships, or part-time work with tuition waiver, to fund a continuation of the study for another year or two? Would this make you a better academic, with better skills under your belt? Or would it only make you look lazy and weird compared to all your peers? I hope you use long-term thinking and consider all options. Good luck!