As correctly noted by the OP, the word ἀββᾶ occurs just three times in the NT and always in the phrase ἀββᾶ ὁ πατήρ, ie, Mark 14:36, Rom 8:15, Gal 4:6.
The word "abba" is a Chaldee/Aramaic word whose definition is given from Thayer in the Appendix below - the vocative form of "Father". BDAG gives very similar information.
The other two words are ὁ πατήρ which is literally, "The Father", referring to God the Father. Thus, the full phrase, ἀββᾶ ὁ πατήρ means "Father (Aramaic) The father (Greek)". It appears that Aramaic speaking people addressed their prayers to "Abba" while the Greek speaking people addressed their prayers to "The Father".
The writers of the NT simply covered both bases in saying ἀββᾶ ὁ πατήρ.
APPENDIX Thayer meaning for ἀββᾶ
Ἀββᾶ (WH (βά), Hebrew אָב father, in the Chaldean emphatic state,
אַבָּא i. e. ὁ πατήρ, a customary title of God in prayer. Whenever it
occurs in the N. T. (Mark 14:36; Romans 8:15; Galatians 4:6) it has
the Greek interpretation subjoined to it; this is apparently to be
explained by the fact that the Chaldee אַבָּא, through frequent use in
prayer, gradually acquired the nature of a most sacred proper name, to
which the Greek-speaking Jews added the appellative from their own