The stories of Ramayana and Dasharatha jataka are very similar. As we all know that valmiki was of dwapar yug, so valmiki Ramayana should be older than Dasharatha jataka. But there is no clear archaeological evidence that valmiki ramayana is older than Dasharatha jataka.
- Ayodhya Kand 109:34
यथा हि चोर स्स तथा हि बुद्ध-
स्तथागतं नास्तिकमत्र विद्धि।
As a thief, so is Buddha. Know that Tathagatas are atheists.
Budha is mentioned in Ramayana so it means that ramayana was written later.
- Kishkindha kand 43:12
तत्र म्लेच्छान् पुलिन्दान् च शूरसेनान् तथैव च |
प्रस्थालान् भरतान् चैव कुरूम् च सह मद्रकैः || || ४-४३-११
कांबोज यवनान् चैव शकान् पत्तनानि च |
अन्वीक्ष्य दरदान् चैव हिमवन्तम् विचिन्वथ || ४-४३-१२
"There in the north, the provinces of Mleccha-s, Pulinda-s, that way Shurashena - Prasthala - Bharata - Kuru - Madraka - Kaambhoja - Yavana shall be scrutinized along with the cities of Shaka and Darada, and then search in Himalayas.
This shloka shows that ramayana was written during the period when Shakas were ruling the country.