Billy Ray Cyrus Wishes Miley A Happy Birthday Amid Alleged Estrangement

Billy Ray Cyrus is highlighting his daughter on her big bday ... sending well-wishes to Miley Cyrus on the same day she turns 32 -- despite their reportedly icy relationship.

The singer-songwriter shared a throwback photo of Miley as a baby ... curled up in his arms on the porch -- smiling up at her pop.

Check out BRC's caption ... sounds like he's reminiscing on the good old days -- before his relationship with his daughter allegedly got complicated.

As we've told you ... the two are reportedly not on the best terms -- sparking rumors about friction after neglecting to thank her dad after winning Best Pop Solo Performance and Record of the Year at the Grammys.

She thanked her mom Tish, sister Brandi and boyfriend Maxx Morando ... but, Billy's name never came out of her mouth.

In more recent months, Miley has talked about her dad ... but, not exactly in a loving context. Instead, MC admitted she got her "narcissism" from her dad -- and, praised her mom for really being the person who raised her.

The fallout between the pair allegedly stems from her parents' divorce ... with Miley growing closer to her mom after she filed to split from her dad.