The relation of that Patristic doctrinal development to pentecostal church tradition today with regard to a particular aspects of belief, worship or practice, e.g. is the Patristic doctrine still effective, or neglected, or is it rejected?
Another component of patristic doctrine was its evangelical element- the idea that true believers ought to spread the faith. This made Christianity unique among its contemporary faiths, and, I'd argue, is a distinguishing characteristic of Pentacostal tradition.
Though your question is under the heading of "Holy Spirit," the question itself asks only about Patristic doctrine in relation to Pentecostal tradition. In answer to this, there is much that falls under Patristic doctrine. One aspect of Patristic doctrine are the establishment of the early doctrinal creeds such as the Nicene Creed. Pentecostal churches and denominations still acknowledge and give allegiance to the Nicene Creed.
If you look at the history of the development of doctrine, it will become clear that the doctrine of the Holy Spirit has not be sufficiently dealt with during the patristic period. We can even say that the doctrine of the Holy Spirit was insufficiently dealt with even during the Reformation and Early Modern period. In light of this, I would say that Pentecostalism has done a great service to Christian doctrine by focusing on the Holy Spirit. Even if the church disagrees with what Pentecostals believe on the Holy Spirit, the focus on the Holy Spirit has been an important corrective.
I think that the main idea which came about during the Patristic period was the identification of the Holy Spirit as a divine power. Some believed the Spirit to be an angel and others believed the Spirit to be a creature. Therefore, what came about for the Pentecoastal church is their beliefin the power of the Holy Spirit and its divinity.
I think if we examine the original beliefs of the Holy Spirit that were first presented in the Patristic time period of church history, we can easily see that the modern day Pentecostal movement has greatly developed and transformed them to add a number of different aspects of theology regarding the Holy Spirit. They have certainly taken the original and developed it massively.
Let me make sure I understand your question. Are you asking whether medieval patristic (i.e. Catholic) ideas about the holy spirit are relevant at all in modern-day Pentecostal (i. e. Protestant) thinking about the holy spirit?