It is a bit confusing, you say you worked for 8 months and got PF contribution for 5 months (?) but you are in doubt as to whether you are/were official staff of the company and also you are bound by the laws since you did not sign any offer letter or confirmation? The query is shown to be from Malaysia.
Since you worked for 8 months in the company you have been an employee of that company for that period. Whether you were counted among Official Staff or elsewhere is an administrative decision but the legal status of being an employee has accrued to you even though you did not sign any offer letter or confirmation. If no PF was paid for the first three months and if you are insistent, a remedy exists by way of complaint to the PF Department. As it is not clear, you are referring to Malaysian laws or Indian Laws, it is better to refrain from commenting further on your legal rights and obligations