According to Thayer’s, the preposition under (ὑπό Strong’s 5259) as used in Romans 3:9 means being “subject to the power of.”

Thayer’s Greek Lexicon

εἶναι ὑπό τινα or τί, to be under, i. e. subject to the power of, any person or thing: Romans 3:9; Romans 6:14, 15; 1 Corinthians 9:20; Galatians 3:10, 25; Galatians 4:2, 21; Galatians 5:18; 1 Timothy 6:1

One way to view Paul’s epistle to the Romans is as a treatise on sin. Tracing sin to its roots, Paul outlines the effect of sin on all humanity.

Romans 5:12 ESV

Therefore, just as sin came into the world through one man, and death through sin, and so death spread to all men because all sinned

Despite its human origin, sin is presented as more than just an act of human disobedience or the product of human choice, but as a powerful corrupting force that shapes human behavior with devastating consequences. Intrinsically tied to man’s carnal nature, such is the power of sin that the knowledge of God’s law serves only to heighten sin’s influence and increase man’s accountability (cf Rom 7:7-20). Without God’s help, the human will alone is helpless against sin’s power, and humanity without exception – subject to its rule.

Romans 7:14-15

¹⁴ For we know that the law is spiritual, but I am carnal, sold under sin. ¹⁵ For what I am doing, I do not understand. For what I will to do, that I do not practice; but what I hate, that I do.

Paul’s arguments regarding sin reinforce his larger point that God alone has the power to free mankind from sin.

Romans 8:3-4

³ For God has done what the law, weakened by the flesh, could not do. By sending his own Son in the likeness of sinful flesh and for sin, he condemned sin in the flesh, ⁴ in order that the righteous requirement of the law might be fulfilled in us, who walk not according to the flesh but according to the Spirit.

According to Thayer’s, the preposition under (ὑπό Strong’s 5259) as used in Romans 3:9 means being “subject to the power of.”

Thayer’s Greek Lexicon

εἶναι ὑπό τινα or τί, to be under, i. e. subject to the power of, any person or thing: Romans 3:9; Romans 6:14, 15; 1 Corinthians 9:20; Galatians 3:10, 25; Galatians 4:2, 21; Galatians 5:18; 1 Timothy 6:1

In Paul’s epistle to the Romans, he traces sin to its roots and outlines the effect of sin on all humanity.

Romans 5:12 ESV

Therefore, just as sin came into the world through one man, and death through sin, and so death spread to all men because all sinned

Despite its human origin, sin is presented as more than just an act of human disobedience or the product of human choice, but as a powerful corrupting force that shapes human behavior with devastating consequences. Intrinsically tied to man’s carnal nature, such is the power of sin that the knowledge of God’s law serves only to heighten sin’s influence and increase man’s accountability (cf Rom 7:7-20). Without God’s help, the human will alone is helpless against sin’s power, and humanity without exception – subject to its rule.

Romans 7:14-15

¹⁴ For we know that the law is spiritual, but I am carnal, sold under sin. ¹⁵ For what I am doing, I do not understand. For what I will to do, that I do not practice; but what I hate, that I do.

Paul’s arguments regarding sin reinforce his larger point that God alone has the power to free mankind from sin.

Romans 8:3-4

³ For God has done what the law, weakened by the flesh, could not do. By sending his own Son in the likeness of sinful flesh and for sin, he condemned sin in the flesh, ⁴ in order that the righteous requirement of the law might be fulfilled in us, who walk not according to the flesh but according to the Spirit.