"This is sampe chart's title"
will break the chart, so that the apostrophe should be escaped by a backslash:
"This is sampe chart\'s title"
and in the code-behind you would need two:
"This is sampe chart\\'s title"
Please refer to the following help article where described different scenarios and cases of handling special symbols
If, however, you are not able to fix your issue after applying the information from the article, I advise that you send us a runnable project
, so we can track it locally. To make things simpler a basic snippet of a chart with a few items with an example string that breaks it will suffice.
the Telerik team
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