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Motivated mainly by certain interesting recent extensions of the Gamma, Beta and hypergeometric functions, we introduce here new extensions of the Beta function, hypergeometric and confluent hypergeometric functions. We systematically investigate several properties of each of these extended functions, namely their various integral representations, Mellin transforms, derivatives, transformations, summation formulas and asymptotics. Relevant connections of certain special cases of the main results presented here are also pointed out.