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As an employer, you have extremely vast discretion when it comes to how you manage your employees. Really the only thing you cannot do is refuse to pay your employees at the agreed upon rate for the hours they have already worked. This means you can't "retain" paychecks for any period of time beyond the regular pay period, and you can't deduct from earned wages.
You CAN, however, terminate employees at any time for virtually any non-discriminatory reason. This power is inherent in all employment because employment is presumed to be "at will" absent an agreement to the contrary. It doesn't even need to be written into your handbook, though of course there is no harm in clarifying. Since employment is at will, there is also no purpose in implementing "trial" periods. An employee is either an employee or they are not, and an employee can always be terminated at any time. There is no meaningful distinction under the law to being a "trial" employee.
In addition to your power to terminate, you can change the terms of employment moving forward. For example, you can reduce an employee's pay moving forward if they have a no-call-no-show, or they do something else wrong. You just want to notify the employee of the paycut in writing, that way there is no dispute as to the rate the employee thought they were working for.
I think this just about covers it. I hope that you find this information helpful. Please do not hesitate to let me know if you have any questions or concerns regarding the above and I will be more than happy to assist you further.
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