I made and object in blender with checker texture but when i try to import it in unreal Engine it only imports with object. The texture is not imported
When you export your FBX in Blender, at the top of the Export FBX dialog, there is an option for how external data is saved ("Path Mode"). click the drop-down for that and choose "Copy". Also click the button next to it that looks like a box ("Embed Textures").
Now your texture will be exported.
NOTE: "Complicated" materials will not be preserved when you export in .fbx format. As a general rule, anything more complicated than plugging an image texture node into a material property will fail in another application. Use only
Principled BSDF shaders and only a single
Image Texture node for any one of its properties--those properties should be limited to PBR-workflow standby's: "Diffuse"/"Albedo", "Roughness", "Normal". You will have to rebuild the rest yourself in the game engine you import the .fbx to.