Transdermal patches can be a very precise time released method of delivering a drug. Cutting a patch in half might affect the dose delivered. The release of the active component from a transdermal delivery system (patch) may be controlled by diffusion through the adhesive which covers the whole patch, by diffusion through a membrane which may only have adhesive on the patch rim or drug release may be controlled by release from a polymer matrix. Cutting a patch might cause rapid dehydration of the base of the medicine and affect the rate of diffusion.
The appropriate strength for each person and situation depends on many factors. For example, babies absorb topical steroids faster than adults, so they may require a low-potency steroid. Areas of the body where your skin touches other skin (think: armpits, rectal area, etc.), as well as sensitive areas like the skin on your eyelids, tend to absorb topical steroids more rapidly, so those regions of the body also usually require a low-potency steroid. However, thick, rough skin on the palms of your hands and the soles of your feet usually absorb topical steroids more slowly than other parts of the body, so those areas typically require a more potent steroid.
You can buy some topical corticosteroids "over-the-counter" without a prescription. For example, for dermatitis, you can buy the steroid cream called hydrocortisone 1% from your pharmacy. Do not apply this to your face unless your doctor has told you to do so. This is because it may trigger a skin condition affecting the face ( acne or rosacea. ) Long-term use may also damage the skin. On your face this would be more noticeable than the rest of your body. So usually only weak steroids are used on the face. Those which are suitable are prescription-only.