The answer is: the Holy Spirit, the Spirit of Christ, and the Spirit of the Father, and these are all the one and the same spirit shared by the three persons of the Trinity.
Romans 8:9:
- εἴπερ πνεῦμα θεοῦ οἰκεῖ ἐν ὑμῖν (“if indeed the Spirit of God dwells in you”)
- εἰ δέ τις πνεῦμα Χριστοῦ οὐκ ἔχει (“but if someone does not have the Spirit of Christ”)
This is evidently the same spirit. If this Spirit dwells in them, then they (i.e., Christians) have that Spirit. First, that Spirit is described as “the Spirit of God,” then immediately after in the same verse, it is described as “the Spirit of Christ.”
Romans 8:10:
- εἰ δὲ Χριστὸς ἐν ὑμῖν (“but if Christ [be] in you”)
Romans 8:9–10 in summary:
- the Spirit of God dwells in [someone]
- [someone] has the Spirit of Christ
- Christ is in [someone]
In Romans 8:11, first the apostle states,
- εἰ δὲ τὸ πνεῦμα τοῦ ἐγείραντος Ἰησοῦν ἐκ νεκρῶν οἰκεῖ ἐν ὑμῖν (“but if the Spirit of Him who raised Jesus from the dead dwells in you”)
Now, the participial phrase τοῦ ἐγείραντος Ἰησοῦν ἐκ νεκρῶν (“of Him who raised Jesus from the dead”) refers to the Father;1 therefore, “the Spirit of Him who raised Jesus from the dead” would be equivalent to saying “the Spirit of the Father.” (Elsewhere, the Spirit of the Father is equated to the Holy Spirit.2) Then, the apostle mentions “His Spirit that dwells in you.” Again, “His Spirit,” referring to the Father’s Spirit, is used elsewhere in reference to the Holy Spirit.3
Footnotes
1 Rom. 6:4, 10:9
2 Matt. 10:20 // Mark 13:11
3 1 John 4:13 cf. 1 John 3:24
Romans 8:9–11 in summary:
- the Spirit of God dwells in them
- they have the Spirit of Christ
- Christ is in them
- the Spirit of [the Father] dwells in them
Summary
The Bible clearly indicates a distinction of persons: “Father, Son, and Holy Spirit.4
Footnotes
4 Matt. 28:19; 2 Cor. 13:14
Christians have the Holy Spirit.5
Christians have the Spirit of the Son (Christ).6
Christians have the Spirit of the Father.7
Christians have the Son (Christ).8
Christians have the Father.9
Footnotes
5 1 Cor. 6:19
6 Rom. 8:9
7 1 Cor. 7:40
8 1 John 5:12; 2 John 1:9
9 1 John 2:23; 2 John 1:9
The Holy Spirit dwells in Christians.10
The Spirit of the Son (Christ) dwells in Christians.11
The Spirit of the Father dwells in Christians.12
The Son (Christ) dwells in Christians.
The Father dwells in Christians.13
Footnotes
10 Rom. 8:11; 2 Tim. 1:14
11 Gal. 4:6 (dwelling implied)
12 Rom. 8:9, 8:11
13 1 John 3:24, 4:12, 4:13, 4:15, 4:16
The Holy Spirit is in Christians.14
The Spirit of the Son (Christ) is in Christians.
The Spirit of the Father is in Christians.15
The Son (Christ) is in Christians.16
The Father is in Christians.17
Footnotes
14 John 14:17; 1 Cor. 6:19
15 Matt. 10:20
16 Rom. 8:10; 2 Cor. 13:5
17 Eph. 4:6; 1 John 4:4
Augustine, “On the Trinity,”18
And it is proved by many other testimonies of the divine words, that the Spirit, who is properly called in the Trinity, the Holy Spirit, is the Father’s and the Son’s.
Et multis aliis divinorum eloquiorum testimoniis comprobatur Patris et Filii esse Spiritum, qui proprie dicitur in Trinitate Spiritus Sanctus.
Footnotes
18 Augustine, Book XV, Ch. XXVI, p. 1092
Because God is Spirit, and there exists a spiritual communion between and indwelling among19 the three persons of the Trinity, the Holy Spirit can be said to be the Spirit of the Father and the Spirit of the Son.
Footnotes
19 perichoresis (Greek περιχώρησις) or circumincession (Latin circuminsessio)
References
Aurelius Augustinus Hipponensis. Patrologiæ Cursus Completus: Series Prima. “De Trinitate” (“On the Trinity”). Ed. Migne, Jacques Paul. Vol. 42. Petit-Montrouge: Imprimerie Catholique, 1843.