Crazy theory, I know. 
It just kind of popped in my head, so I might as well write it all out.
I'm not even sure if this is true or not, but here I go:
*takes deep breath*
We don't know about too much about Minato and Fugaku's relationship, but I can predict it to be like the off and on relationship Naruto and Sasuke had. I could predict they were friends because Shikaku also seemed to be part of the "Konoha 11 or whatever number" during Minato's time.
And again, we don't know too much about Fugaku compared to Minato, but I can predict they may have had a few fights off and on, but nothing compared to the rivalry between Naruto and Sasuke, Hashirama and Madara and Ashura and Indra. Or atleast, not that we know of so far.
Hagoromo already said that Ashura and Indra were reincarnated into different people overtime, the only two we know are Hashirama and Madara and Naruto and Sasuke, but the other one can be Minato and Fugaku.
I believe this can be true, because Fugaku seemed to control everything through his clans name and eventually planning a coup d'état against Konoha, thus making him the reincarnation of Indra. Minato seemed to be a little more loving compared to Fugaku, making him the reincarnation of Ashura. I assume that he also had an off and on rivalry with Fugaku, but nothing compared to Hashirama and Madara or the latter.
Again, everything here may not be entirely true, I'm just combining facts with predictions.
(P.S. I apologize for my terrible explaining skills. Zzz)

It just kind of popped in my head, so I might as well write it all out.
I'm not even sure if this is true or not, but here I go:
*takes deep breath*
We don't know about too much about Minato and Fugaku's relationship, but I can predict it to be like the off and on relationship Naruto and Sasuke had. I could predict they were friends because Shikaku also seemed to be part of the "Konoha 11 or whatever number" during Minato's time.
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And again, we don't know too much about Fugaku compared to Minato, but I can predict they may have had a few fights off and on, but nothing compared to the rivalry between Naruto and Sasuke, Hashirama and Madara and Ashura and Indra. Or atleast, not that we know of so far.
Hagoromo already said that Ashura and Indra were reincarnated into different people overtime, the only two we know are Hashirama and Madara and Naruto and Sasuke, but the other one can be Minato and Fugaku.
You must be registered for see images
You must be registered for see images
I believe this can be true, because Fugaku seemed to control everything through his clans name and eventually planning a coup d'état against Konoha, thus making him the reincarnation of Indra. Minato seemed to be a little more loving compared to Fugaku, making him the reincarnation of Ashura. I assume that he also had an off and on rivalry with Fugaku, but nothing compared to Hashirama and Madara or the latter.
Again, everything here may not be entirely true, I'm just combining facts with predictions.
(P.S. I apologize for my terrible explaining skills. Zzz)