The coin has been tossed three times each showing up head.The probability of getting head the fourth time should be one half but should be we instead saying it 1/16 considering the previous tosses?
If I understand your question correctly you are asking whether the 4th toss is dependent on the first 3 - the answer is no. Every toss is independent, so the probability of a fair coin landing on heads will be always 0.5. Note that it is perfectly normal to get "clusters" of the same side (e.g. heads showing up x times in a row) given that you toss the coin "enough" times.