I implemented my ANN using SKlearn module's class MLPClassifier. Fitting it on some data and testing it on a very specific subset of said training data, it gives a score of 1.0, but actually using the ANN to generate outputs for said testing data almost always gives incorrect output. What could be the possible reasons for this? I am using this ANN as a memory network and there is never a case when input is out of training data.
You're testing your neural net with data from the training set, of course it will get you great results. But you're neural net is now trained for a specific data and is unable to make generalization. This is known as Overfitting.
You should either split your data into test/train or use another technique to estimate your NN performance. A good technique is K-fold Cross validation.