Can we have a dataset with slight difference in target values for same value of feature variable?
I'm not sure what's the context of your question but there's no problem with the approach you've outlined. Different values of y for the same unique value of x (over different rows, such that for example you have: x = {1, 1}, y = {1, 2}) are a natural result of the noise usually assumed in the model you fit (e.g. $y = x + \epsilon$).
Hope this helps.