After the Pope declined to appoint him Archbishop of Armagh, the diocese in which he served as Vicar General, he was instead installed as the second Bishop of Philadelphia in 1819.

Conwell took up the post at an advanced age and spent much of his time there feuding with the lay trustees of his parishes, especially those of St. Mary's Church in Philadelphia.

The two sides partially reconciled by 1826, but the Vatican hierarchy believed Conwell had ceded too much power to the laymen in the process and recalled him to Rome.

Although he retained his position, Conwell was compelled to relinquish actual control to his coadjutor bishop, Francis Kenrick.

[2][3] Conwell was well-educated, being fluent in Latin, French, Spanish, and Italian, but had a reputation as a preacher of only modest ability.

[19] A letter from the Pope sided with Conwell but, after initially agreeing to leave the diocese, Hogan reversed himself and stayed on.

[21] The pro-Hogan faction prevailed at St. Mary's trustee elections that year amid bloody rioting between parish members.

[19] The next year, 1823, some Hogan supporters convinced a local woman to bring a paternity suit against Conwell, but the charges were dismissed quickly and the complainant was convicted of perjury.

[19] In an 1824 letter to the National Gazette, Hogan proposed the creation of an "American Catholic Church" with more independence from Rome.

[21] In hopes of healing the schism, in October 1826, Conwell partially capitulated to the trustees, yielding to them the right of determining salaries and of vetoing his appointments.

When word of the compromise reached the Holy See, the Vatican also objected, condemning Conwell's surrender of episcopal rights.

[25] By this time, as Arthur Ennis wrote in 1976, the "old and confused" Conwell considered leaving the diocese if he could secure another see in Ireland.

[26] In 1827, the Vatican's Propaganda Fide formally rejected Conwell's pact with the trustees, condemning Hurley's role in the process, as well.

[28] The following year, the Vatican appointed Francis Kenrick as Conwell's coadjutor bishop with the right of succession and named him administrator of the diocese.

[28] Conwell never gave up his titles or his claim to exercise authority in the diocese, and his relationship with Kenrick remained rocky.

[29] He received permission to resume performing liturgical functions without any say in administration, and spent his remaining years in seclusion and prayer.