I have a Li-ion battery(3.7V and charging Voltage 4.2V, 1800mAh) and I bought a Lipo battery(3.7V and charging voltage 4.2V, 2500mAh) for my smartphone. And I want to create a homemade battery case. So I am thinking to connect these batteries in parallel series to increase the battery capacity. is there will be a problem for that the one is Li-ion and other is Lipo? And can I make a power house using Li-ion and Lipo in the same circuit ?
I wouldn't connect any battery to your phone but the one designed for it. The charging circuit is designed for the specific battery.
You can technically probably connect a Li-Ion and LiPo battery in parallel with a properly designed charger, but it is not recommended. Usually only identical cells are connected in parallel or series.
One big issue is current hogging in the constant-current charge phase. Initial charging of a lithium ion battery is done at constant current, generally expressed as some rate like "1C" which means charging a 2500 mAhr battery at 2.5 amp (i.e., a one hour charge rate). If you put two cells in parallel, you might think you could increase the charge rate, but unless the cells are identical, one of them may hog most of the current. So if you are charging with 5A, it might be that 1.5 amp goes to one battery and 3.5 amp goes to the other: exceeding it's safe limit.
Another issue is with charging voltage. Lithium ion chargers switch to constant voltage mode when the battery gets to a certain pre-set voltage, nominally 4.2 volts. However, different anode types have slightly different voltages, in the 4.1-4.2 range. If you look at the data sheets for li-ion charging circuits, they usually have some mode selection to trim the voltage for slightly different cell types. If you connect two batteries with different voltages in parallel, you could overcharge one.
Finally, lithium ion chargers are designed to stop charging when the constant voltage phase drops to a certain minimum current to avoid trickle charging, which will cause overcharging and cell damage. If you put batteries in parallel, that threshold needs to be adjusted. If the batteries are not identical, that could be off.
In practice, if you set your charger to charge at the rate of the smaller cell, and you make sure that the maximum voltage of the two cells is the same, nothing bad is likely to happen. However, charging will take about twice as long as if you used identical cells, so this is not usually done. Multi-cell battery packs are usually made from brand new identical cells ideally from the same manufacturing lot, and permanently connected so that they age together.