ahamkAra and asmitA are two concepts that one encounters in sAdhanA, and the distinction between the two puzzled me at one stage in my practice. Therefore, I try to clarify the difference between the two for the benefit of others on the path. There is a parallel between ahamkAra and asmitA, and Mind and Consciousness. Essentially, what ahamkAra is to the mind, asmitA is to Consciousness. Therefore, until the mind is transcended, it will be difficult to gain a first-hand understanding of asmitA.
So let us try to understand ahamkAra first, so that by analogy we can get an idea of what asmitA is. As discussed in other articles, ahamkAra is explained in Sanskrit as 'aham karomi iti ahamkArah": literally, I do in this way is defined ahamkAra. So ahamkAra is a part of the antahkaraNa, which we loosely call the mind. In meditation, ahamkAra is encountered in the manomayakosha and is and examined from the vantage of the vijnAnamayakosha (the sheath of the buddhi: the discriminating, non-attached observing faculty of mind). We can then see how we construct the notion of "I act" in various scenarios. Here the mistaken identity of actor-ship is revealed because we realize that our true self is deeper than that part of the mind that says "I act".
Once all the koshas are penetrated and one is beyond even the Anandamayakosha in samAdhi, there is an experience of Consciousness, but it is still individuated. One might say this is the experience of jIva, or the kAraNa sharIra with the latent impressions temporarily at rest. Here the limitation of Consciousness in an individuated sense is experienced. This is what is meant by asmitA: which literally means the state of I exist (asmi: I am, and asmita: the state of feeling I am). Through bindu vedhana one goes even beyond this to the state of pure Consciousness devoid of any individuation, where the experience is of pure Existence: the direct experience of Om from which one emerges with the feeling of pure "Is-ness". So to truly understand asmitA, one has to experience "Is-ness" devoid of the "I" in "I am".