The manipulation of aqueous droplets has a profound significance in biochemical assays. Magnetic field-driven droplet manipulation, offering unique advantages, is consequently gaining attention. However, the phenomenon relating to diamagnetic droplets is not well understood. Here, we report the understanding of trapping and coalescence of flowing diamagnetic aqueous droplets in a paramagnetic (oil-based ferrofluid) medium using negative magnetophoresis. Our study revealed that the trapping phenomenon is underpinned by the interplay of magnetic energy (E-m) and frictional (viscous) energy (E-f), in terms of magnetophoretic stability number, S-m = (E-m/E-f). The trapping and nontrapping regimes are characterized based on the peak value of magnetophoretic stability number, S-mp, and droplet size, D*. The study of coalescence of a trapped droplet with a follower droplet and a train of droplets) revealed that the film-drainage Reynolds number (Re-fd) representing the coalescence time depends on the magnetic Bond number, Bo(m). The coalesced droplet continues to remain trapped or gets self-released obeying the S-mp and D* criterion. Our study offers an understanding of the magnetic manipulation of diamagnetic aqueous droplets that can potentially be used for biochemical assays in microfluidics.