We discover a population of short-period, Neptune-size planets sharing key similarities with hot Jupiters: both populations are preferentially hosted by metal-rich stars, and both are preferentially found in Kepler systems with single-transiting planets. We use accurate Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) Data Release 4 (DR4) stellar parameters for main-sequence stars to study the distributions of short-period (1d<P<10d)Kepler planets as a function of host star metallicity. The radius distribution of planets around metal-rich stars is more “puffed up” compared with that around metal-poor hosts. In two period–radius regimes, planets preferentially reside around metal-rich stars, while there are hardly any planets around metal-poor stars. One is the well-known hot Jupiters, and the other one is a population of Neptune-size planets (2R⊕≲Rp≲6R⊕), dubbed “Hoptunes.” Also like hot Jupiters, Hoptunes occur more frequently in systems with single-transiting planets although the fraction of Hoptunes occurring in multiples is larger than that of hot Jupiters. About 1% of solar-type stars host Hoptunes, and the frequencies of Hoptunes and hot Jupiters increase with consistent trends as a function of [Fe/H]. In the planet radius distribution, hot Jupiters and Hoptunes are separated by a “valley” at approximately Saturn size (in the range of 6R⊕≲Rp≲10R⊕), and this “hot-Saturn valley” represents approximately an order-of-magnitude decrease in planet frequency compared with hot Jupiters and Hoptunes. The empirical “kinship” between Hoptunes and hot Jupiters suggests likely common processes (migration and/or formation) responsible for their existence.