Some groups advocate that there is a “second filling” or a “Holy Spirit baptism” that believers will get after (at some time later) they have been born again. There is no Scriptural support for this claim.
While Cornelius experienced a special “baptism” by the Holy Spirit, it was done as a special sign to the early church to show that Gentiles were to also now receive the Holy Spirit. This was a one-time special case event to show the early apostles (who were nearly all Jews) that God’s grace now extended to the Gentiles. From the cited reference: 
The purpose for which Cornelius was granted the Spirit was to demonstrate to the Jews that God was ready for the gospel to be offered to the Gentiles — which circumstance constituted a problem in the thinking of the Hebrews.
In effect, the Holy Spirit baptism given to Cornelius was analogous to the pouring out of the Holy Spirit upon the Jewish apostles at Pentecost. So, the gospel hereby and hereafter spread out to go to the gentiles also. Amen!
 See also: Jackson, Wayne. “Is Holy Spirit Baptism Available Today?” ChristianCourier.com. Access date: November 8, 2018. https://www.christiancourier.com/articles/519-is-holy-spirit-baptism-available-today