After the calling of your case we met with you and discussed the sentence along with the appeal process.
在您的案件宣判之后，我们与您见面并讨论刑罚和上诉的程序。

次序应该是：宣判，判刑，上诉。

你的案件开审（被立案/被受理）以来

下面是call的法律定义之一：

To convoke or summon by public announcement; to request the appearance and participation of several people—such as a call of a jury to serve, a roll call, a call of public election, or a call of names of the members of a legislative body.

因为都是小案件，基本上就是跟法官见一面就结案了，

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Note added at 8 hrs (2020-02-14 05:28:40 GMT)
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比如警察把告票提交给法庭，法庭联系你，商定开庭时间，这个过程就是calling of your case，实际上相当于“确定受理/予以立案”的意思。