Never punish your Morkie puppy for an accident by shoving its nose in the mess and yelling or spanking it. The puppy won't understand why you're angry, and Morkies are small so you can easily injure them through physical punishment. Also, the Yorkshire Terrier side of your Morkie might cause it to get aggressive if you hit it. It's much more effective to concentrate on positive reinforcement rather than punishment.
Learn to read your Morkie's body language, and you'll soon be able to tell when it needs to go outside. Morkies will get restless, pace or walk in circles, and start to sniff around for a spot to potty. When you see these behaviors, immediately take the puppy outside to the correct spot.
Morkie puppies are a cross between a Maltese dog and Yorkshire Terrier. True to their Maltese side, they tend to be playful and energetic and thrive on attention and affection. From the Yorkshire Terrier side, they inherit a territorial nature and some aggressiveness. You will need to take your Morkie's size and temperment into account to potty train it effectively. The process takes some time and patience, but if you do it correctly it will pay dividends when you have a well-trained adult dog.
Make sure you give your Morkie enough opportunities to relieve itself. All puppies are small, and Morkies are tinier than most because they result from a cross of two small breeds. They have small bladders and don't have practice at "holding it" yet. You need to take your Morkie outside at regular intervals, giving it a verbal signal like, "Potty time!" that it can learn to associate with the process. When you take it out, be patient and give it enough time to go. Don't play with it or pet it, as this is distracting. Stand quietly and watch for signs that indicate your Morkie is ready to relieve itself.
When your Morkie puppie goes potty in the correct place, shower it with praise. Like their Maltese relatives, Morkies have a strong desire to please their owners, so positive reinforcement works much better than punishment. Your Morkie will soon learn that when it relieves itself in the right place, it will earn an enthusiastic reaction.
Crate your Morkie when you are not home, or confine it to a small area where it will not cause damage if it has an accident. Keeping your Morkie in a crate or restricted area lessens the chance of an accident, because it won't want to soil its sleeping spot. It it does go, you'll be able to easily clean the mess. You will need to offset the confinement with plenty of opportunities for exercise once you get home. Their Yorkshire Terrier background gives Morkies lots of energy, and they need regular chances to expend it.
Feed your Morkie on the same schedule every day. If you stick to regular feeding times and take away uneaten food after your puppy has had time to eat, you will encourage a regular potty schedule. Morkies are small, so it's important to control the portion to make sure your puppy doesn't get obese, as well as to regulate its potty schedule. You'll know when you need to take your Morkie outside for potty time, because it will tend to go at the same time each day.
Don't get upset if your Morkie is doing "submissive urination." Many puppies leak some urine when they get excited or nervous, especially those with smaller bladders. This is involuntary, so it's not a real "accident." Your Morkie should outgrow the problem by the time it is 6 months old. In the meantime, don't make a big fuss or punish it because it can't help the leaks.