SECOND CENTURY (PART 2)
(iii) THE CHANGE OF LOCAL LEADERSHIP
With bishops emerging as pseudo apostles, their focus appears to have changed to overseeing congregations, in a city or region, rather than as an elder in a local congregation. This role change necessitated a leadership transformation in each local church.
Deacons, as we dealt with in chapter two, were initially appointed to fulfil certain administrative functions within the early Church. They were subordinate to elders, but were required to meet the same rigid qualifications (Acts 6:3; 1Tim. 3:8-13). Deacons were responsible for distributing the Church’s charity, and later assisted elders to serve the elements of Holy Communion from house to house. 
The term deacon (Gk. diakonos) means slave, underling, or helper.  Although with the appointment of the seven men in Acts 6 the title “deacon” was not given, there can be little doubt that these men were indeed deacons. Some streams of the Church view deacons as a clerical order within the Church to which they refer to as the diaconate. The Roman Church for example, according to Eusebius, took such a strict view about the diaconate that up until the fifth century they only ever appointed seven deacons.  While in the early fourth century, the Greek Council of Neocaesarea ruled that any given city could only boast seven deacons.  The argument for a limited number of deacons within the early church is supposedly supported by Paul’s general lack of instruction to establish them in all churches. For example, in writing to Titus, who was installed as the overseer of Crete, Paul instructs him to appoint elders, but says nothing to him about appointing deacons in the churches.
The reason I left you in Crete was that you might straighten out what was left unfinished and appoint elders in every town, as I directed you.
(Titus 1:5 NIV)
But historically it can be reasonably established that deacons were indeed generally in each local church. Ignatius, writing about 60 years after the close of the New Testament, about the Antioch and Asian churches, refers to them having a monarchical bishop, together with presbyters and deacons.  Professor Chadwick states-
Apart from the historical evidence for deacons becoming a clerical order within local churches, there is the strong Biblical evidence from the New Testament that Paul did indeed appoint deacons in local churches.
Paul and Timothy, servants of Christ Jesus, To all the saints in Christ Jesus at Philippi, together with the overseers and deacons
(Philippians 1:1 NIV)
I commend to you our sister Phoebe, a servant (diakonos) of the church in Cenchrea.
(Romans 16:1 NIV)
Deacons, likewise, are to be men worthy of respect, sincere, not indulging in much wine, and not pursuing dishonest gain.
(1Timothy 3:8 NIV)
The Didache, which scholars now trace to the period 70-110 AD,  deals with Christian conduct and protocols for hosting visiting apostolic and prophetic ministries. It says in regard to deacons being in each local church-
Deacons appear to have originated as the assistants to elders. As the concept of the bishop being a priest developed, deacons were eventually forbidden from celebrating the eucharist (Holy Communion) with worshipers, firstly by the Council of Arles (314), then the Council of Nicaea (325). But it appears that prior to this it was commonplace for them to be officiating over the eucharist in churches not served by a resident bishop. This was especially so in rural churches. 
sourced from https://www.andrewcorbett.net
As deacons were often the ones visiting the sick, dispensing charity among the unfortunate within the church, their role also developed into a more pastoral one. As this was taking place, the role of the bishop was being developed to the point that while churches had resident presbyters, the bishop tended to oversee an entire city, region or province. Certain cities were singled out as more important and influential that others, and thus the bishops of these cities were recognised as having more authority than their fellow bishops. These cities included, Rome (the capital of the Empire), Alexandria, and Antioch.