I have sterling silver watch model3141 SR927W with three push button on right side. One I lost.Where I can buy this push button????

No spares inside?

There is no one selling them. You could use a generic silver button, or contact Mr. Cole himself.

https://www.google.com/search?q=Kenneth+Cole+silver+rivet+buttons

Contact

https://www.kennethcole.com/pages/contact-us

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yes. wrong battery possibly...
395/399 = SR927SW/SR927W

The 395 is a lower power output but same voltage (1.5v). The power spike of shorting might have caused a spike in the watch electronics.. make sure they are right polarity too. These batteries are not high current items, but maintain their voltage over the 5+ year lifespan. The S and SW are basically interchangable except for the higher amerage output.

Most likely a SILVER OXIDE SR927W or equivalent

If it uses the citizen miyota 6s21 movement like many do, then it's a SILVER OXIDE SR927W or equivalent

See https://www.fossil.com/content/dam/fossil/PDF/watchinstructions/Fossil_Watch_Instructions_EN_US.pdf

The file is a compendium of instructions for a large number of Fossil movements, but it is unclertain which movements the model CH-2331 and CH-2698 watches use. However, movement OS10 (page 15) appears to be the only one that matches the dial layout, button layout and also has a date window as the CH-2331. The watch has a quartz analog mechanism and uses one SR927W 1.55-volt silver oxide button cell. Silver oxide cells have low current output, but very long shelf life, so if the stem is pulled out completely when the watch isn't being worn, the battery could last many years. Scan the instructions to match up the CH-2698 with a movement number. A good guess from examining photos of the face of a CH-2698 watch would be movements OS20 / FS00 or VD53.

What make and model of watch is this?

in normeal time mode...Push silver button on lower left of watch 3 times, seconds start flashing. push lower right silver button 2 times hour starts flashing. push upper right silver button until you scroll through the time desired, either A, P instead of H for military time.

Go to the Rotary web site http://www.rotarywatches.com/en/service/rotary-watch-servicing and contact them to discuss your problem.

good morning ! to open your sterling watch,use knife for snap in case back of your sterling watch ! good luck !..