Is there any machine learning algorithm that can solve this problem? I have a data set of 100000 samples with binary output.

I would like to study the impact of Col_A (a continuous feature) on the output result. 

Col_A has values from 0 to 7000000 and when I add this feature to my classifier it gives bad accuracy. I have tried z-score and scalar number but it doesn't change a thing.  

I would like to try another method to solve this problem.

I made some plot visualization to my data and I found that there is some range in which the majority of the outputs are negatives. ie. when col_A is ranging between (0 - 200), between (2500 - 2800) and between (5200-5400) the majority of outputs are negatives.

I would like to create a new feature to specify which category my Col_A is in, instead of using Col_A.

PS: I can't use if--else rules because I don't know where to delimit these ranges, I have just analyzed the previous values from my plot. but I need to have a dynamic method for getting those categories.

Is there any type of clustering that can solve this problem?

Does neural network help for this case?
You want a supervised approach. Clustering will not care about your target variable and perform arbitrary splits that don't help.

Likely a decision tree can be helpful here, if you use a good implementation that can split the same feature multiple times (to break it into intervals). There are other approaches you could try, such as piecewise regression etc.