I am a first time researcher and naively submitted to an OA predatory journal (on BEALL'S LIST) which requests a publishing fee. Having read the terms and conditions, there was no comment stating that I needed to pay if accepted for publication and did state that i retained copyrights to my work. My work was accepted and they requested the publication fee but I have now found that my work is already on their website without the fee being paid or me signing anything. Is there anyway to retract my work without being penalised?
It totally depends on your jurisdiction. However, as pointed out by Solar Mike, they made an "invitatio ad offerendum" (like at the bakery, where they invite you to make an offer (i.e. want to buy) a bread or similar). By submitting, you declared to make an offer and they accepted it and published it. So they fulfilled their part of the contract and your part (payment) is still open.
You can still try to retract your paper by sending an email to the editor and maybe it's worth a gamble to not pay. Your institution should be able to help you with this question
Normally, you also need to confirm to its publication (and say goodbye to your copyrights). So I think even though you have submitted it, you hold the right to let it be published or not. Use an affirmative language and make it clear that it is not about the price. Stand firm with your request.
Not exactly same, but I once agreed to be a reviewer and then figured out they are a predatory conference/publisher, I regretted it immediately but thought I had to brace it (while they put my name on their website and I felt like I screwed up my career). Luckily for me they sent totally unrelated papers for me to review and when I said I am not even remotely an expert on this subject, they said well you could still do it and I saw my ticket out and demanded firmly my name to be deleted from their site and in the end they did.
That being said, this depends on their reputation but if it is not too crappy, a free online access paper has a good chance of more citations.