Source of Ichigo's shinigami power

Question

In Bleach chapter 673 it says that Juha is Ichigo's true father, so with his mother also being a Quincy,

...where did Ichigo get his shinigami powers from? (Up until this chapter, I thought he got his shinigami powers from Isshin.)

Answer 1

Short answer, from his father, Kurosaki Isshin.

Long answer is provided below with history of Ichigo's life.

This answer contains massive spoilers

First of all, you need to understand that Ichigo is unique in that he was born from a Quincy mother (Kurosaki Masaki) and a Shinigami father (Kurosaki Isshin, formerly Shiba Isshin). Because of this, he has the power of both Quincy and Shinigami.

During her mother's high school age, Aizen was experimenting with Hollowfication and created a hollow called White, who caused Hollowfication on Hirako Shinji and other captains of Gotei 13 to turn into hollow. The hollow, White, was then sent to attack Shiba Isshin (Ichigo's father, his family name was Shiba before he married Masaki and uses her family name). Kurosaki Masaki rescued Isshin from the Hollow but was Hollowfied herself. This caused Ichigo to have hollow powers in him as shown by White having a similar looks to Ichigo's Hollowfication form.

Isshin married Masaki and Ichigo was born. It was shown that Ichigo was able to see spirits since he was elementary school student where he saw Grand Fisher's bait and attempted to save it thinking that it was a girl who tried to drown herself. This attempt of his caused his mother's death.

Years passed and Ichigo is now 15 years old. A hollow attacked his house and Kuchiki Rukia saved him by transferring her Shinigami powers to him. This act awakens his dormant powers that he inherited from his parents. He later lost the powers Rukia lend him from Kuchiki Byakuya's attack. He regained it after training with Urahara, but this time it was his own dormant "Shinigami" powers. Notice the use of double quote there.

Ichigo fought the Shinigami to save Rukia, learned Bankai in the process. Then he fought Aizen's Espada to save Orihime, and eventually Aizen himself to save Karakura Town. To fight Aizen's godly powers he learned a forbidden technique from Kurosaki Isshin, called the Final Getsuga Tenshou. This technique caused him to lost his "Shinigami" powers.

He then regained his "Shinigami" powers after the captains of Gotei 13 and vice-captains Abarai Renji and Kuchiki Rukia transferred power to Ichigo during the end of the Fullbringer Arc. Then the Quincy attacked, lead by their king, Ywach (some called him Juha Bach). During the fight his Zanpakuto was destroyed and to forge it he went with the Zero Division to meet the maker of Zanpakuto, Nimaiya.

It was during the forging process that it was revealed that the so called "Shinigami" power he has been using was actually his Quincy powers, which also explains why Ywach looks so much like Zangetsu. Now he awakens his true Shinigami power which Zangetsu has been suppressing.

So in conclusion, the "Shinigami" power that he has been using before he broke his Zanpakuto was actually his Quincy power which he inherited from his mother. His real Shinigami power is obviously from his father Kurosaki Isshin since Isshin is also a Shinigami. He can use Hollowfication since his soul was infused with Hollow Kurosaki Masaki sealed, the hollow White, inside her body.

As for what it means by

In Bleach chapter 673 it says that Juha is Ichigo's true father, so with his mother also being a Quincy,

it is more in a spiritual meanings. Just like Odin was called the Allfather (means father of all), Ywach is the father of all Quincy since all Quincy's powers was born from him. This makes him Ichigo's father in spiritual means, just like Odin was father of Norse people.