Resignation During Probation Period

I've been working with this company for 6 months, till to date no confirmation letter has been issued by the HR even though they load me with tonnes of work. if am still not confirm, can I tender my resignation under the 2 weeks period?
Another question, any company who issue the confirmation letter to their employee, to my understanding, both party must sign on the confirmation letter right? Employer & Employee . Does the confirmation letter valid if the employer purposely back dated the letter and issue to employee saying that am a confirmed staff after I tender the resignation letter? because once am confirmed, it will be in one month noticed.

If you have a good opportunity or has decided to leave the organisation, you can tender resignation stating that since you are not confirmed as on date of resignation, the notice period as per the appointment letter/terms will be 2 weeks.

Signing of both parties on confirmation letter is not mandatory. However, the company may sign in back date that confirmation was given to you long time back, but in that case the company has to prove that such letter was actually issued to you or you have received the same. If such acknowledgment is not available, you can surely take the plea that such letter was never issued to you.
Since you are in probationary period, you may resign with the notice period as stipulated in your offer letter (I assume that you have offer letter).
You may consult a professional to draft your resignation letter too if you are unable to handle yourself.