The harmonium is great for giving you a visual introduction to how music works, but if you're trying to be a vocalist, your best bet for achieving good command over the notes is to make sure you don't use the harmonium as an accompanying instrument when you're practicing. The harmonium can easily become a crutch because it plays all the notes for you and you can see what note is being played.
Practice with a tanpura instead. The tanpura does not play the notes themselves, so it forces you to pay attention to what you are singing. Also, the tanpura produces overtones of many of the important notes in the octave, which allows your voice to resonate best at the right frequencies. So, by learning to listen to the tanpura and to your voice against the tanpura, you can learn to sing in tune over time.
Another tip for learning to sing in tune is to record yourself singing and then play it back and listen to it. This makes it easier to hear your mistakes, and you can then work on those mistakes.
Using the harmonium as a crutch may actually be the only way to mess up the process of achieving command over your notes despite years of training, because almost every step of training in Indian classical music strengthens your command over the notes just naturally speaking. All you have to do is to pay attention and put in the time.
Having said that, there are also exercises specifically designed to speed up the process of becoming familiar with the notes.
In the Hindustani system, there are sequences of notes called palta or alankar that you can practice for each raga. Some of these exercises may be taught to you by your teacher, but you can create your own simple or complex sequences, and the more sequences you practice, the more familiar you become with the different kinds of intervals and relationships between the notes.
Here is a video of Pt. Ajoy Chakrabarty training young Kaushiki Chakraborty to sing different types of paltas at different speeds.
There are also what are called sargam geet or swarmalika, which are simple sargam compositions in each raga. However, you don't need specific compositions for this. You can take any existing composition with lyrics and practice it as a sargam geet, and that way you become more conscious of its notation. If you take it upon yourself to figure out the notation without help, you also get good training in note recognition.
As your training progresses, you will learn to sing ragas. A part of the training process is to repeat after the teacher. The teacher usually sings complex phrases in aakar or lyrics, and unless you understand what notes are being sung, it can be very difficult to repeat accurately. Ear training is not the main focus of this process, but it is something that happens naturally as a by-product.
In this video, Pt. Ajoy Chakrabarty is teaching Kaushiki to sing Raag Basant Mukhari. He makes her repeat each phrase until she gets it just right. At one point she's not able to repeat what he is singing precisely, so he stops her and asks her to tell him the notes he is singing.