Pasajın zeminindeki mozaik desenler antik döneme ait izler taşıyor.

Breakdown of pasajın zeminindeki:

• pasaj + -ın (genitive “of the”) → pasajın = “of the passage”
• zemin
  • -i (3rd-person possessive, linking back to pasajın) + -nde (locative “in/on”) + -ki (relative adjective marker)
    → zeminindeki = “which is on its floor”

So pasajın zeminindeki literally means “on the floor of the passage,” and it functions as an adjective modifying mozaik desenler.

In Turkish, X’e ait Y means “Y belonging to X.” It’s built from:

1. X in the dative case (suffix -e/-a),
2. the adjective ait (“belonging”),
3. and Y (the possessed noun).

Thus antik döneme ait izler is literally “traces belonging to the ancient period,” i.e. “traces from the ancient period.”

The verb taşımak means “to carry.”

• The -ıyor suffix marks the present continuous tense.
• In Turkish, the present continuous can also express general truths or descriptive states, not just an action in progress.

So taşıyor here is best understood as “carries” (or “contains”), describing a standing characteristic: “(the patterns) carry traces.” You could also use the aorist taşır, but taşıyor emphasizes the observable state of currently having those traces.

• Mozaik = “mosaic” (loanword from French)
• desenler = “patterns” (plural of desen)

In Turkish, a noun placed directly before another noun acts like an adjective without any extra suffix. Thus mozaik desenler = “mosaic patterns.”

(Note: mozaikli desenler would mean “patterns that have mosaic on them,” a slightly different nuance.)