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We present our follow-up observations with GRANDMA of transient sources revealed by the Zwicky Transient Facility (ZTF). Over a period of six months, all ZTF alerts were examined in real time by a dedicated science module implemented in the Fink broker, which will be used in filtering of transients discovered by the Vera C. Rubin Observatory. In this article, we present three selection methods to identify kilonova candidates. Out of more than 35 million alerts, a hundred sources have passed our selection criteria. Six were then followed-up by GRANDMA (by both professional and amateur astronomers). The majority were finally classified either as asteroids or as supernovae events. We mobilized 37 telescopes, bringing together a large sample of images, taken under various conditions and quality. To complement the orphan kilonova candidates, we included three additional supernovae alerts to conduct further observations during summer 2021. We demonstrate the importance of the amateur astronomer community that contributed images for scientific analyses of new sources discovered in a magnitude range r′ = 17 − 19 mag. We based our rapid kilonova classification on the decay rate of the optical source that should exceed 0.3 mag d^−1. GRANDMA’s follow-up determined the fading rate within 1.5 ± 1.2 d post-discovery, without waiting for further observations from ZTF. No confirmed kilonovae were discovered during our observing campaign. This work will be continued in the coming months in the view of preparing for kilonova searches in the next gravitational-wave observing run O4.

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