It is not just Shri Ram from the Ikshavku dynasty whom Ravan feared. It is long before the birth of Shri Ram itself that he fought with an ancestor of Shri Ram.
Bhagwan Vishnu incarnated as Shri Ram in the Ikshavaku dynasty to kill Ravan, thus bringing glory to the Raghuvansh. The lineage into which he chose to take birth was a line of great kings, who were known for their courage and also their conduct of Dharma in the three worlds. One such king is Mandhata who was known for his valour. He was a son of the Suryavansha king Yavanashv.
Mandhata was born from the right side of his father’s abdomen after Yavanashv accidentally drank the sacred sacrificial water which his queens were supposed to partake for giving birth.
Mandhata got the name when Indr offered his finger for sucking when he was crying for milk. (मान्धाता – meaning ‘drink me’ )Mandhata mastered the entire knowledge of the
Vedas and Military sciences. He acquired impenetrable armour, a अक्षय त ीर and the
अजगव bow which belonged to Bhagwan Shiv. With all his valour, he came to be known as a powerful warrior in all the three worlds. Not only known for his valour, he was known for his generosity too. He performed 100 Aswamedha Yagnas and 100 Rajasuya Yagnas for the welfare of his kingdom and also took care of all his subjects dearly.
At the same time, Ravan has acquired powerful boons from Brahma Ji, and began to harass the three worlds with his arrogance and ego. He started conquering all kingdoms and reached Ayodhya. He challenged Mandhata for war, and thus the war began between the two. The war was a very ferocious one and Mandhata successfully defeated all the mighty warriors of Ravan like Shuk, Akampan, Mahodar, Virupaksh and many more. Seeing that, Ravan himself came to battle.
Both the warriors fought with each other with a determination to defeat each other. They attacked each other with different mighty weapons and arrows. Ravan starts fearing Mandhata, who is dominating him in the battle field and to win over him, takes the aid of ब्रम्हास्त्र. To counter the ब्रम्हास्त्र, Mandhata aims the पाशुपतास्त्र. With the most powerful arrows aimed at each other, the three worlds start trembling and fear annihilation. To save the three worlds from the terror of the two arrows, Rishi Pulasty and Rishi Galav intervene the battle and ask Mandhata and Ravan to stop waging the war.
The rishis explain to Mandhata that Ravan is destined to be killed by his descendant Shri Ram and ask him to put an end to the war. Mandhata obeys the command of the rishis and stops the war with Ravan. Since them, Mandhata comes to know by the name of रास्त्यादस्त्युुः
(Trasyadasyu) the one who was feared by demons
Thus, Ravan not only feared Shri Ram, but also his descendant. The reason why he abducts Mata Sita through deceit also is for the same reason that he knows he can never conquer the Ikshvaku kings face to face. But, his arrogance and ego grows so high that he does not recognise that through his actions, he has bought the doom of himself and his whole clan. All his actions right from the times earlier before Shri Ram add up to his sins and finally become the cause of his destruction.
(Source- Uttarkand- Shri Valmiki Ramayan)