How is Aryama linked to the Pitrs, and how is his role different from Yama's?

Question

It is said that the Vedic god Aryama, the son of Aditi, is the foremost among the Pitrs or manes. This has also been stated by Lord Vasudeva in the 10th chapter of the Bhagavad Gita:

अनन्तश्चास्मि नागानां वरुणो यादसामहम्।
पितॄणामर्यमा चास्मि यमः संयमतामहम्॥२९॥

Among snakes I am Ananta, and Varuna among gods of the waters. Among the manes I am Aryama, and among the maintainers of law and order I am Yama (King of death)

What is Aryama’s role as the foremost of the Pitrs and how is he linked to them? What are his divine duties?

1. If Aryama is linked to the Pitrs, then what is the difference between the role of Yama (who gives jeevatmas a place depending on their karma) and Aryama? (We can see Krishna has distinguished Aryama as being the head of the Pitrs and Yama as a Dharmaraja.)
   
   

2. Like Yama, is Aryama worshipped during Shraddha rituals/ death rituals of a person? And if the answer is affirmative, then what is the purpose of worshipping him (again linked to what is his role, that we worship him)
   
   

3. The Puranas talk of many divine Pitrs (with their wife Svadha) being Barhishada, Agnishvatta, etc. Aryama being an Aditya does not feature among these groups and is considered entirely separate. Is he the ruler of these Pitrs (if he is the ruler then how is Yama king) Or does he help them in their respective roles?

Kindly note the question is not a duplicate of Who is god Aryama in the Vedas?; Reason: the linked question asks who he is, whereas my question seeks clarifications, not as to his identity, but to his role as a Pitr, comparison with Yama and his worship, which do not find mention in the aforesaid question.

Answer 1

The word pitr may have usages.

Dharmashastra (religious law) — Pitri in Dharmashastra glossary Source: Google Books: Manusmṛti with the Manubhāṣya Pitṛ (पितृ):—It has been said that ‘ one shall offer balls to the Pitṛs.’ Now the question arises—Who are these ‘Pitṛs ?’ The term ‘pitṛ’ has several meanings, and denotes ‘progenitor’;

it is used in the sense of the relative term, ‘father’; it is also used in the sense of one’s father and other relations that have died before. Further, the term ‘pitṛ’ also denotes a particular Deity ; and in this sense, it would stand for an unchanging eternal being. The term ‘pitṛ,’ thus having several meanings, the Text proceeds to specify what is meant by it in the present context. (See the Manubhāṣya verse 3.220)

So Aryama would be foremost of the Deities , and unchanging eternal being by that Manubhashya.

And Yama would be the foremost of the netherworld.

Quoted as required for clarity:

ध्रियमाणे तु पितरि पूर्वेषामेव निर्वपेत् ।
विप्रवद् वाऽपि तं श्राद्धे स्वकं पितरमाशयेत् ॥ २२० ॥

dhriyamāṇe tu pitari pūrveṣāmeva nirvapet |
vipravad vā'pi taṃ śrāddhe svakaṃ pitaramāśayet || 220 ||

While his father holds, one should make the offering to the previous ancestors; or, he may feed his own father at the Śrāddha as a Brāhmana.—(220).

Answer 2

aryaman means Sun. aryaman is singular in Accusative Case, and its plural in same Case is aryamAn.

Aditi's children are the 12 names for Sun.

Source: https://gaurav101.medium.com/aditi-and-the-%C4%81dity%C4%81s-9f90ab20027a

About the relation between aryaman and yama, being sons of Aditi, they are brothers. While aryaman is the lord of the pitris, yama was the first pitri.

Source: https://www.wisdomlib.org/definition/aryaman

Source: https://sreenivasaraos.com/tag/pitri/

Source: https://sreenivasaraos.com/tag/pitri/