Is a justification of deductive reasoning possible? If so, please tell me how because whenever I try to form a justification of deductive reasoning I end up committing the fallacy of circularity.
This question comes up quite frequently. I recommend you to read Conifold's answer to Is there a deduction analog to the problem of induction? and my answers to What justifications have been given for using particular systems of logical calculus? and References for the justification of the use of Logic
I am inclined to accept Hume's argument : Hume presented us with a dilemma: we cannot justify induction inductively, because to do so would be to show that whenever the premisses of an inductive argument are true, the conclusion must be true too-which would be too strong; and we cannot justify induction in- ductively, either, because such a 'justification' would be circular. I propose another dilemma: we cannot justify deduction inductively, because to do so would be, at best, to show that usually, when the premisses of a deductive argument are true, the conclusion is true too - which would be too weak; and we cannot justify deduction deductively, either, because such a justification would be circular. (Susan Haack, 'The Justification of Deduction', Mind, New Series, Vol. 85, No. 337 (Jan., 1976), pp. 112-119 : 112.)
Note that Hume's statement of the crux about justifying deduction itself rests on deductive argument throughout.
Haack herself seeks to find her way round Hume. Also Michael Dummett delivered a long, complex and speculative British Academy Paper on 'The Justification of Deduction' in which he looks for a suitable validation of deduction. Both papers really are too long and subtle to summarise adequately here. I provide the references.
Susan Haack, 'The Justification of Deduction', Mind, New Series, Vol. 85, No. 337 (Jan., 1976), pp. 112-119.
Michael Dummett, 'The Justification of Deduction', reprinted in Michael Dummett, Truth and Other Enigmas. Oxford University Press (1974).
David Hume, A Treatise of Human Nature, ed. D.F & N.J. Norton, Oxford : OUP, 2009, II.4.1 ('Of scepticism with regard to reason'), 121-5.
Justification of deductive reasoning is impossible, as is justification of any other kind of reasoning. Justification is an alleged process that shows an idea is true, or probably true or good or something like that. But any argument makes assumptions and uses rules of inference, which may or may not be correct. So any idea you get from those assumptions and rules of inference is a guess. Any attempt to justify the assumptions and rules of inference would run into the same problem.
This problem was solved by Karl Popper. The demand for justification should be rejected root and branch. Knowledge is created by guessing solutions to problems and then criticising the guesses. Ideas are sorted not by justification but by criticism. See the references given here for Karl Popper and David Deutsch for more explanation: