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Reconstructing 3D geometry from \emph{unoriented} point clouds can benefit many downstream tasks. Recent shape modeling methods mostly adopt implicit neural representation to fit a signed distance field (SDF) and optimize the network by \emph{unsigned} supervision. However, these methods occasionally have difficulty in finding the coarse shape for complicated objects, especially suffering from the ``ghost'' surfaces (\ie, fake surfaces that should not exist). To guide the network quickly fit the coarse shape, we propose to utilize the signed supervision in regions that are obviously outside the object and can be easily determined, resulting in our semi-signed supervision. To better recover high-fidelity details, a novel importance sampling based on tracked region losses and a progressive positional encoding (PE) prioritize the optimization towards underfitting and complicated regions. Specifically, we voxelize and partition the object space into \emph{sign-known} and \emph{sign-uncertain} regions, in which different supervisions are applied. Besides, we adaptively adjust the sampling rate of each voxel according to the tracked reconstruction loss, so that the network can focus more on the complicated under-fitting regions. To this end, we propose our semi-signed prioritized (SSP) neural fitting, and conduct extensive experiments to demonstrate that SSP achieves state-of-the-art performance on multiple datasets including the ABC subset and various challenging data. The code will be released upon the publication.