I think they add a य to connect the verb root आ- (or जा-) to the verb ending, because those two verb roots end with a vocal sound आ and the verb ending also begins with a vocal ए for 3rd person singular (यह ; वह) or एं for plurals ( हम; आप; ये; वे). Doesn't work with मैं nor तुम subject since verb ending begins with vocal ऊं or ओ respectively. This may be a general rule for vocal ending verb root. But it does not work with irregular verbs लेना or देना: to form the future tense, we take the verb root ल- or द- but not ले- or दे- as usual, respectively ( verbs to take and to give): वह लेगा ; नेहा लेगी ; वे देंगे ; हम देंगी ; मैं लूंगी ; तुम दोगे । That is a guess, please someone correct me If I'm wrong.
You took it in a wrong and very lengthy way. Actually, the word "आएगा" is the correct word. To understand it better I have to give brief information about hindi alphabet here. Like english hindi also have vowels and consonants.There are 36 consonants and 13 vowels in Hindi alphabet. "अ, आ, इ, ई, उ, ऊ, ऋ, ए, ऐ, ओ, औ, अं, अः" all these 13 words are hindi vowels and also used as "hindi matra" (vowel signs) with consonants like क ख ग घ च ... When using vowels as vowels sign like 'इ' 'have vowel sign ( ि) with 'क' it becomes 'कि' same as
क +ी = की क+ु = कु
क+ू = कू क+े = के
And so on. For more detailed information on each hindi matra you can check the link given below
I am also providing the link on how are they written in english language