If p-value is 0.00 and Cliff delta is small, can my null hypothesis be rejected? When I run non-parametric tests on my dataset, I get p-value as 0.0 (so, p < 0.05,  also p<0.005) and Cliff's delta value is around 0.3. So can I confidently say the null hypothesis rejected?
I am running python program. 
 A: When coming to conclusions about data, it is important to look at effect size or other ways to assess the practical importance of the effect.
However, when assessing the null hypothesis all that matters is the decision rule†.  That is, if your decision rule is "If p < 0.05, reject Ho.", then if p < 0.05, then reject the null hypothesis.  That's it.
The p-value and the effect size address two completely different ideas.  For example if Group A has values (1, 2) and Group B has values (2, 3), comparing these groups results in a Cliff's delta of 0.75, which is a large effect. But obviously in this case there is little evidence to reject the null hypothesis that the two groups are stochastically equal.
In your case, you have good evidence to reject the null hypothesis (p < 0.005). And you have a small-to-almost-medium effect size.  There is probably a lot of other information to bring to bear on arriving to conclusions, such as can be derived from histograms, plots, and descriptive statistics. But also practical considerations:  is this effect size --- or difference in medians, etc. --- meaningful?

† Along with meeting assumptions of the test, and so on.
